You discredit your argument with your first sentence. 

As someone who is the parent of both genders, all of my kids have faced some sort of discrimination in the labour force because they were not the preferred gender, or the right ethnicity. We can do a lot better as a society in levelling the playing field.

Yes, you are right, advancing rights for one demographic should not come at the expense of another. And that goes for gender, race and sexual identity.

But the females (c'mon - snowflake girls?) in my family, peer group, and social circle are not "demanding domination" nor trying to keep men down. They are just trying to keep the gains their mothers (and fathers) fought for, in the face of a world looking to subjugate anyone "not like them".