Huh? Biology absolutely does mandate that. Unless wires have been completely crossed here, when you say "women should not be disadvantaged", you are presumably talking about employment / work.
The entire purpose of employment is to output work that is useful to other people / society at large. If you are not doing that, there is no reason for you to be gainfully employed by anyone else. Therefore, please note that any time I say "productivity" in the rest of this comment, I mean it in the sense of doing productive work for other people, e.g. employment.
As a side-effect of childbirth, women lose productive capacity. Men do not. This is not a societal choice, it is a physiological reality. It will continue to be true up until the moment women no longer need to carry a baby around in their wombs for 9 months in order to bring new humans into the world. Note I'm just talking about pre/perinatal here, not long-term child rearing.
Any "disadvantage" occurs naturally as a result of loss in real usefulness (for a time) when it comes to employment. Now, you want to compensate for that natural loss in productivity by mandating that men artificially lose productivity in the form of paternity leave. I agree with you that this is probably[1] a good idea. But not wanting to overcompensate for actual biological differences is not sexism. This clearly doesn't fall into sexism because it doesn't apply to all women. It only applies to women that can + want to have children. The discrimination is not based on sex, it's based on a demonstrable loss in productivity that occurs naturally and by choice.
Again, this is very much unlike the disadvantage experienced by black Americans before the Civil Rights Movement, which was not a result of natural processes but rather a result of completely arbitrary bigotry and absolutely not in any way, shape, or form brought on by a choice made by black Americans.
[1] I say probably here because obviously paternity leave only applies to men who are having / have had children, so you will continue to have a similar problem (discrimination based on a loss in productivity), except now the sides are not "women having children" vs. everyone else but rather "people having children" vs. everyone else (i.e. people that don't want children). As I said though, I agree and still think this is better than the completely natural version of events, where only the woman side of the equation loses productivity, because at the end of the day in situations like these it is both the woman and the man who are choosing to bring a child into the world. And even though it is a choice to do so, it is obviously the kind of choice which we need people to make otherwise society will cease to exist, which is why I am happy to compensate for the loss in productivity due to this choice. That being said, once test-tube babies are both easy (easier/safer than natural childbirth) and normalized, I probably won't be able to countenance advantaged maternity/paternity leave (at least before the "birth" of the baby), because then it will be an entirely optional choice and you would be effectively punishing people that choose to have babies in the test-tube fashion.