I think that by reducing the the gene pool they would be creating unforeseen problems, or at least creating an environment where problems will have a vastly reduced chance of being fixed.
No biologist here, but would it really reduce the gene pool to reduce the fraction of men to 10%? Information stored in DNA doesn't depend on gender, and I don't know of anything which men contribute apart from their DNA (while women also have some additional information which only women can store or something, I've forgotten the details, I think it's in the egg cells).
I am also not a biologist, and I was just guessing, as indicated by "I think". I don't know what would result from eliminating a majority of half of the breeding population of a species, but without the diversity my guess is that some rare genetic traits found in those that remain might be amplified. I want to try to calculate it, but I am not good at such things.
If because of this the world population was lowered, only then of course the size of the gene pool would decrease, but we have more than enough humans, that should certainly not pose any problems
If you get rid of nearly 50% of the population wouldn't the overall population be reduced?
I was thinking more along the lines of a slow change over a few generations, where everyone would be discouraged to have boys, so there would be more girls born, without influencing the total birth rate (which is going down anyway here in middle Europe and I guess in the US too). I think that would be possible, like it happens I've-forgotten-where, where they tend to abort girls. It's also possible to naturally influence the ratio by accurately choosing the time to have unprotected sex (I've forgotten which one is which, but either the sperm cells carrying Y-chromosomes or those carrying X-chromosomes live longer than the other, but are a little slower on the other hand).
That way, as far as I know, no genetic information would be lost (in another than the usual way, there is always new information added and old lost).
Of course, if you just sterilized 8/9 of men today (magically, I'm just assuming), then the population would certainly decrease, probably a world war would break out.
But still: I don't think men's genetic information is statistically different from women's, I don't think there would be /biological/ problems when you would remove most of the men. There would probably just be lots of other problems.
(citation: in the past there were much less humans and they got by just fine)
I wonder if we would be able to keep advancing in certain fields if we drastically reduced the overall population to a number that is less overwhelming and destructive. I like to think that we could at least maintain where we are now.
I think something which works for gender equality shouldn't be named after one gender anyway.
I am probably wrong, but I always thought the name was due to the situation that led to feminism, where "normal" had them not as equals.
That's an interesting train of thought, spontaneously I would think that we could get by just fine with half of our current population, but it certainly depends a lot on how that half of the population would be removed. But if it happened no faster than a hundred years or so? Probably most of the problems would be due to too many old people who need to be taken care of, but that problem would only exists during the reduction, once the population stabilizes at a lower level that problem would solve itself again.
If, say (next thought experiment), Africa was wiped out, I'm not sure how badly the rest of the world would be affected in the long term. If it was America, China or Europe it would probably kill the world economy for quite a while, thus causing problems for the survivors. But I'm no economist either, so I guess we would need to ask one of those.
I'm pretty sure you've got it right with the origin of the name feminism, but what they fought for was always equality, not the reversed situation. So I would have looked at it like this and named stuff accordingly: There are people who fight for equal rights for all humans (be it gender/"race"/social status/amount of money in their possession). Those people would see the gender inequality and thus decide they needed to make the female gender stronger. But their actual/abstract goal wouldn't be "Strenghten the female gender", it would be "Eradicate cultural, economical and other non-biological gender-inequalities.".
And that's important from the beginning on, just /because/ of what is happening now, to prevent it: Some people just going on and on in areas where equality has already been reached.
Edit: By the way: Yes, sometimes I like walls of text too. No I haven't gotten anything better to do, and if you disagree, then I don't care. *looking at those keyboard guys*