In order to flourish, humans need to be both subjectified and objectified-- that is, they they need to feel like they are in control of their life and that their wellbeing is taken as an end in itself by others (subjectified) but they also need to feel useful and wanted by others (objectified).

Of course they ideal balance between these two paradigms probably varies greatly between individuals and between groups. But I think it is plausible that our culture, in general, over-objectifies women and under-objectifies men. I don't think this is actually that controversial, most narrative protagonists are men, most people who make money from their physical attractiveness are women. Bosses tend to be men, secretaries tend to be women. Traditionally men headed families, went to work and made the important decisions. Traditionally a woman's role was to support her husband, cook for him, raise his children and look nice.

Now, if we assume that, whatever the ideal ratio of objectification to subjectification is for women, our culture over objectifies it becomes clear why feminists would oppose female objectification (one would also suspect that outspoken feminists would be among the most over-objectified relative to their ideal). The person doing the objectifying is contributing to patterns and trends that, on balance, make life worse for women. Conversely, men might be under-objectified and that is why they don't understand why women object to certain instances of objectification. For example, most men probably want to be stared and desired just for their bodies more often than they are right now.

I don't mean to suggest that the situation is symmetrical for men and women, exactly. It seems likely being over objectified is worse than being under objectified (a free person who isn't needed or wanted by anyone is probably still better off than most slaves). Men and women may also, on average, prefer different levels of objectification.

In general, if we want a culture that provides something close to the ideal amount of objectification and subjectification for everyone we probably want a system that doesn't objectify whole groups-- better for people to get the objectification they need on an individual basis which should be better calibrated.