When their argument is proven wrong, they explain how they're still correct by explaining the reasons that their argument is wrong

Hi. I was just reading about the pay gap recently (not a topic I care too much about, but my curiosity was randomly sparked, as I never looked much into the topic before) and, as I began listening to both sides go back and forth, I noticed this sort of thing happening frequently:

PRO-GAP
This percentage difference in what men and women are paid proves that the pay gap is real and the correlation is sexism.

ANTI-GAP
That percentage is over-exaggerated and is substantially lower once you factor in the alternative correlations of education, hours worked, women not choosing higher-paying jobs, et cetera.

PRO-GAP
But those factors themselves are the result of sexism. I.e., high school girls are discouraged from taking the math and science classes that lead to high-paying jobs. Thus, sexism is still the correlating cause of the pay gap.

The original argument here was about whether the pay gap is real and due to sexism. However, after the ANT-GAP shows that the percentages only count raw numbers and aren't as high once adjusted to include other factors, the PRO-GAP changes the argument into one about how school girls are discouraged from entering high paying jobs.

Since the PRO-GAPs new argument isn't proved to be right or wrong, the argument then becomes sidetracked to be about whether or not it's true that society is influencing school girls to be less interested in lower-paying jobs.

While I can understand why the PRO-GAP would do this and can follow their logic in doing so, something about their argument and how it sidetracks into a new (albeit very related) argument felt off to me in a very fallacy-ish way. And it felt familiar, like I've heard similar arguments being handled in the same manner (although, granted, I can't remember any off the top of my head) in the past.

I was wondering if this actually is a fallacy? And, if so, does it have a name that I'm not recalling?

Thanks!

Perhaps some Moving the Goalposts  going on here. But also sloppy argumentation. Here is how I might respond:

This percentage difference in what men and women are paid proves that the pay gap is real and the correlation is sexism.

Actually, the percentage difference "proves" no such thing; it is the fact that is attempting to be explained. It only proves that there is a X% average difference in pay between men and women. The reasons for this are extensive and not as simple as "sexism." While sexism likely is a contributing factor, the role of sexism tends to be highly exaggerated and other factors such as chosen vocations are much more significant factors.

But those factors themselves are the result of sexism. I.e., high school girls are discouraged from taking the math and science classes that lead to high-paying jobs. Thus, sexism is still the correlating cause of the pay gap.

I can address that, but first, do now acknowledge that the percentage difference in what men and women are paid does not prove that the pay gap is real and the correlation is sexism?

This is how you prevent moving the goalposts. It is fine to address new points; this is how arguments progress. But one must acknowledge that they made a bad argument or made factual errors before moving on.

The central point imo is that the original argument is a proxy, using ambiguous terms. That there is a pay gap is not evidence of why it exists, but unless the terms are well-defined, the argument can come down to "pro-pay-gap" sounding like one in favor of something when the position is the opposite, and the "pro" position refers to the proxy, the implied explanation (sexism) as if it were properly contained in the phrase.

It is a common popular-media short-hand that's revealed in other areas of discussion. We see the ambiguity in many variants of global warming discussion, for example, so that "pro-global-warming" is the position of people who think that global warming is caused by human industry and CO2, and not that they are in favor of global warming. It's similar (worse imo) to using "climate change" in place of "human-caused climate change", as if they meant the same thing.

Insist that the discussion use objective terms, imo, to keep from wandering into a bull-session.
Dr. Bo's approach is one way, but here's another, using the same pair of PROGAP arguments

PRO-GAP

This percentage difference in what men and women are paid proves that the pay gap is real and the correlation is sexism.

I'm not inclined to defend sexism, but can explain the pay gap without it, noting other factors. Can you?

PRO-GAP

But those factors themselves are the result of sexism. I.e., high school girls are discouraged from taking the math and science classes that lead to high-paying jobs. Thus, sexism is still the correlating cause of the pay gap.

It sounds like you're opposed to sexism, as am I. But we were talking about the pay gap.

The fallacy is ambiguity. By insisting on staying on topic (pay gap), the discussion may be useful. IMO, it disarms the opponent's dilatory intent.

This is not a logical fallacy, either way. In the PRO GAP case, it seems to me to be simply jumping the gun, i.e., stating a cause for a problem without any evidence. I guess this could be a kind of logical fallacy. The cause could be sexism, but it could be something else. The ANTI GAP case is definitely not a logical fallacy. This is usually the narrative around an econometric analysis, based on a hypothesis, which is that the gap in pay could be due to a number of other factors, including sexual discrimination (not sexism; sexism is an overall attitude, the crime tested in these analyses is discrimination; you can have sexism without discrimination). If you want to complain about a problem, you can say it is all based on sexism. If you want to solve a problem, you need a more complete description of the causes.

The point is to separate discrimination in the hiring decision from other external factors. If there are two candidates, and the male has more education and experience than the female candidate, he is likely to be more productive and profitable. Same if a job requires substantial physical strength. The decision to hire the male in these cases is not discrimination (or sexism). You can make the case that the educational system favors males, but that is still separate from the hiring decision (and today there are more women pursuing higher education than men). So is occupational choice, or the choice to leave the workforce to raise children. So an econometric analysis separates out ("holds constant") the portions of the hiring decision that are due to education, occupational choice, work history, and other factors. If all these are controlled for and there is still a gap, we assign the cause to hiring discrimination.

Yes, the other causes may or may not be based on sexism. But these analyses are usually made against the suggestion that we simply legislate that employers hire men and women equally regardless of qualifications. This would be very inefficient economically. A better solution is to address each cause at its source. For example, in terms of occupational choice, we need to change the cultural norms steering women into lower paid occupations, or, alternatively, we should pay these occupations at a higher rate (we need to value teachers more). Or we should find a way to credit homemakers with work experience so they are not at a disadvantage when the reenter the workplace. But these are separate from the hiring decision. So econometric analyses are not a logical fallacy, they are actually scientific tests to uncover the truth.