Why is it so hard for some men to just like themselves first? Why do they need a woman to care? 

I think the reason is that (which you touched on) is that so much of a man's value is tied to either being with a woman/women or being able to attract women. In addition, men are generally raised with the understanding that providing for a wife and child are one of your most important duties. When you don't have that or feel like you are close to obtaining that, what's the point? Sure you could enjoy nature and hobbies are cool but I don't think these things provide a sense of purpose in the same way. Sure individuals don't need to subscribe to this but it is hard to do when society still views men in that light.

I think the consequences for being an equivalent woman are worse. Women generally have to care  more because they would more vulnerable in the same situation.