Paternity leave? Its not natural
Of course, some supporters of men's rights will support paternity leave, some won't. This demonstrates how the perpetual drive for 'equality' can devide even those who have an otherwise close ideological alignment.
However, I want to consider another side to this story: does the quest for 'equality' actually result in more freedom in socity? I don't think it does.
For example, with an expansion of 'rights' such as paternity leave (or even with the existance of generous maternity leave for female employees), someone has to pay for it. Your 'rights' end up being my responsibility. Has freedom increased overall? No, you've just shifted freedom away from one person and towards another.
Equally, I think that by seeking to manipulate and engineer society, feminists and leftists risk creating un-expected effects. Science supports the notion that complex systems (be they organisms, the biosphere or societies) opperate in unpredictable and non-linear ways. Sometimes what seems like an increase in the freedom people enjoy can result in an overall diminution of freedom. For example, in the West women have the right to dress however they please (even, to a great extent, within the workplace, where women have a much greater lattitude than men to wear casual clothing). Part of this apparent freedom has resulted in women wearing high heels in order to make themselves appear taller and sexier. Many women, however, find such high heels uncomfortable or even dangerous or harmful to their skeleton. But if you are a woman, and you are surrounded by other women - in the workplace or the nightclub - who are all wearing high heels, not wearing them might make you seem less sexy or less likely to get promoted (I actually believe that, aside from differences in effort and motivation, disparity in workplace promotions is driven more by height than sex). So the freedom to wear high heels ends up resulting in the obligation to wear them. Interestingly, if you could somehow take away this 'freedom', whilst many women would complain, many would rejoice and find themselves MORE free.
Equally, freedom for women to wear what they like can result in a loss of respect for women in general, which in turn might be experienced by women as a loss of freedom!
My solution: we need a balance between individual freedoms and the considerations of the group or society as a whole.