Most people look for reciprocity in relationships. That includes friendships with the same gender. As in men care about their friends, but not men outside that group.

Some people do help strangers. They do volunteering and donate stuff. Most of the people who do that for both genders are women.

Your problem seems to be about wanting women to find any men attractive regardless of how they are treated and to put men first in the hopes that, maybe, if they work hard enough, a man would take notice and "pick them". That is, like it used to be when women needed to marry because they wasn't allowed to work or have money on their own. But things doesn't work like that. Not even before.

If you want people caring about each other, you might need to start by modeling that. But considering that even paying taxes to finance public healthcare is too much for some people but paying for wars is not, I do think that the problem is not on the left, but in the system.