I think that it is not that people don't have empathy with men. As a group, society has empathy with men. The problem is with individual men. People rarely have empathy with strangers (both men and women). You develop empathy with people you are close to. You need to work in a relationship with others for those others to care for you. But many men aren't taught how to develop those relationships, so they struggle to find connections and people who care for them. And they depend on the women in their lives to do that for them. In turn, the women might feel that as a burden, because there is no reciprocity as the men might not have been told how to nurture the relationship and expect the women to care and fix those problems while focusing on the things they perceive as their "area". As in "I work and bring money, everything else is on my wife".

The good thing is that you can listen to your friends (both male and female) and show empathy with them. See who reciprocicate and put more effort on those people. Eventually, you would have a group of people who would care about you. But expecting that from the start is like a stranger expecting you to work for free. You can choose to do it as a nice gesture, but it shouldn't be expected. Also, if you do it and it is not valued, you stop. This is the same.

It is not that women don't care about men's problems. But they have their own problems to deal with. Expecting them to prioritize men's problems when men haven't prioritized women's problems, doesn't work. On individual level is different, since I might reach out and help a male friend who has shown me appreciation and care. But I won't do the same for other men who are basically strangers because I'm human and my time and energy are limited. Also, if I help someone and that someone never helps me, I would eventually stop because I'm no masochist.

Be nice and pay attention to who is nice with you. I guess that sums it all.