The errors of left-wing and right-wing ideologies
To fix terminology: the left-wing ideology is "progressive/liberal", while the right-wing is "conservative".

Here I will consider only politicians or other persons who sincerely believe in these ideologies (at a given time in their lives). I think that the advocates of both ideologies are mistaken about certain things. However, they are mistaken in a rather different manner and about rather different things. It appears to me that there is a certain bizarre symmetry in their mistakes as well as in their successes.

1. Believers in the left-wing ideology are mistaken about the actual results and consequences of the economic and social policies they advocate. (They are just as mistaken about the policies advocated by the political right).

A typical scenario: Prices of item X have suddenly increased for whatever reason. Left-wing politicians now say that "the people demand fair prices and affordable X" and "big corporations must stop the profiteering". The government sets a price ceiling on X. Immediately a shortage of X results, and a black market for X develops with prices much higher than before. This consequence appears to be wholly unexpected to the politicians involved. However, they deny that the shortage was a consequence of their price-control policy, and call for more regulation to fix the new problems.

Another example: In order to combat teenage pregnancies and venereal disease among the poor, it is proposed to make sex education mandatory in high schools, and to distribute condoms for free among the students. The consequence of this measure is an increase in venereal disease and teenage pregnancies. However, the proponents of sex education deny this causal relationship and call for even more sex education and more condoms to be distributed.

In order to combat racial segregation and low educational achievements of black students, it was mandated that all colleges have a certain quota of black students. The percentage of black students who successfully finish college subsequently decreased, and the ethnic segregation and tensions among students increased.

In order to make health care affordable to the poor, Great Britain nationalized health care and made it free to everyone. As a result, people now have to wait many months to get medical treatment, even for serious conditions that require immediate attention (e.g. cancer operations). Medical care has become less accessible, as a consequence of a measure designed to make it more accessible. The same thing happened to medical care for war veterans, administered for free by the American Veterans' Administration.

2. Believers in the left-wing ideology correctly understand the moral force of the arguments they use to justify the proposed policies.

Here are some typical left-wing arguments: Prices are high because the sellers or the producers are "greedy". Almost all of the country's wealth is owned by just 1% of the population because those people are "unfairly privileged". Large numbers of young people are unemployed because the "society" does not have "enough jobs" for them. Homeless people live in the streets because housing was "not made affordable". Ethnic group X is not proportionally represented in occupation Y because of "ethnic discrimination".

The left-wing solution is to prohibit high prices on housing; to take wealth away from the rich and give it to the poor; to subsidize jobs or college education for young people; to enforce ethnic quotas.

These arguments appeal to just two basic moral feelings [1]:
the weak and the vulnerable must be protected, and
everyone has equal rights.
(The remaining four basic moral feelings, listed below, are mostly unused by the political left.) Even though the arguments are technically incorrect and are contradicted by abundant evidence, their emotional and moral appeal is unmistakable.

History shows that these arguments are perennially convincing to large numbers of people in all countries and in all epochs. If we consider it the job of a politician to represent the opinions and feelings of certain parts of the populace, we find that the left-wing politicians certainly do represent the opinions and feelings of large numbers of people.

Left-wing parties have often used this to their advantage, getting elected by a landslide based solely on moral and emotional appeal.

3. Proponents of the right-wing ideology correctly understand the consequences of the social and economic policies they advocate (as well as the policies advocated by the political left).

Right-wing politicians know that lowering taxes on "the rich" will create jobs and lead to increased tax revenue; that abolishing minimum wage will eliminate high unemployment among the young and the poor; that abandoning "affirmative action" quotas at colleges will reduce ethnic tensions and improve minority outcomes; and that replacing sex education by abstinence education will diminish venereal disease and teenage pregnancies.

Right-wing politicians also know that most left-wing parties, if unchecked in their thirst for political power, will lead the country to implementing an ideological dictatorship accompanied by economic misery, - a social system known as "socialism" or "communism".

If we consider it the job of a politician to lead the country towards long-term prosperity and social harmony, we find that the right-wing politicians certainly do propose measures that will achieve those goals.

Right-wing governments are usually successful in improving the economy, reducing crime and social tensions, etc.

4. Believers in the right-wing ideology are mistaken about the efficacy of the arguments they can use to justify the proposed policies.

This mistake is subtle. A conservative politician cannot easily explain why the proposed policy will be beneficial. In some cases, the causal relationships are quite complicated. The politician cannot create a high level of emotional and moral appeal by reciting an economics textbook.

So, conservative politicians usually appeal to core moral values and to tradition. The following four moral feelings are emphasized by conservatives [1]:
freedom of private life, thought, and action within law;
obedience to recognized authority;
loyalty to family, friends, allies, country; and
religious belief in the sanctity of human life and soul.
Essentially, conservative politicians say "we need to live as we lived 100 years ago, with small changes due to modern technology". They talk about "making America great", "return to the core values", the Constitution, hard work, family values, and God.

Naturally, these somewhat vague pronouncements are vulnerable to attack from the left, whose discourse is highly theoretical and involves references to science, technology, and (Marxist) economic and social theory. However, the right-wing ideology cannot respond to this attack in the same way (i.e. through a theoretical discourse), because the right-wing ideology is not based on an articulated intellectual theory of the same kind as the left-wing social theory.

To make this subtle difference more clear, let us ask what are the fundamental pictures of the society in both ideologies. [2]

The left-wing picture is that there is a reasonably simple social theory that explains why certain problems occur in the society and how to solve them. ("The rich are unfairly privileged and have exploited the poor, therefore they now must pay their fair share." - "High prices on X are due to excessive greed; to make X affordable, a price control must be imposed." - "Crime is due to oppressive society; to reduce crime, more rights need to be given to people." - "Minority students obtain a worse education because they go to segregated schools; to improve this situation, all schools need to be desegregated." - etc.)

The left-wing proposal for the society is to make reforms that will immediately implement the measures prescribed by the social theory.

The right-wing picture is that the workings of a society are far too complicated for anyone to understand in any degree of precision. Existing social theories do not agree with evidence. For example, the market operates with millions of prices for individual items, and all these prices change every second or even faster. It is impossible for any single person or organization to know enough to be able to determine the "most efficient" or "fair" price at any given time. Basically, people's behavior is too complex to be described by simple theories (such as "high prices are due to greed"). Millions of people make decisions such as where to live, what to study, etc., and no one can presume to know the "best" decisions for every person in every situation. History shows that measures intended to change people's behavior often give paradoxical results. According to the conservative ideology, we must accept that quick solutions of social problems will probably not be found; we can only hope to achieve acceptable trade-offs and slow, incremental changes. It takes centuries for the society to develop organically, at its own pace, into a direction that gradually improves life for all. No one would be able to impose the modern condition on a society by any reform 300 years ago. In each country, the developments in local customs, traditions, culture, social life, and economics are tightly connected. No one can seriously presume to have articulated a "theory of society"; the only way to discuss society is to look at the existing tradition and to learn from history of your own country and other countries.

The right-wing proposal for the society is to continue its complicated, organically developing activities, with perhaps some small and tentative adjustments of the kind that have previously proven their efficacy.

In the left-wing mind, the society has been already quite adequately understood - by a select group of intellectuals who formulate a social theory. This theory is sometimes referred to as "social science", to lend it more credence. In this way, a left-wing advocate can attack the conservative position as "unscientific" or "against progress". Indeed, conservatives cannot say that they disagree with liberals about the theory of society - conservatives usually do not attempt to articulate any theory of the same nature as the left-wing social theory. To shield themselves from this attack, conservatives are therefore prone to express skepticism about science in general and "social progress" in particular. However, this is not a very convincing repartee today, due to today's mass accessibility of science and technology and, especially, to the mass ignorance of economics and history.

So, it is in this way that the right-wing politicians overestimate the degree to which their arguments can be convincingly and appealingly articulated.

Electoral defeat often comes unexpected to right-wing politicians. They sincerely do not understand how it can be that many reasonable people fail to become convinced by their argumentation.

References:

[1] J. Haidt. The righteous mind: why good people are divided by politics and religion. 2012.

Haidt is a psychologist with a sincere left-wing political preference.

[2] T. Sowell. A Conflict of Visions: Ideological Origins of Political Struggles. 2002.

Sowell is an economist with a sincere right-wing political preference.