Capitalism is about free markets. The arrangement of wage labor is an emergent result of allowing people to enter only into economic relations they consent to.

To take care of others for free is entirely fine, if it’s what you want to do. That doesn’t conflict with capitalism at all. The only difference is that under a free market people do that when they choose to, not when they are compelled to.

And what actually happens is that people choose to a lot.

That's the cartoon version of capitalism just like how "socialism is when the government does something" is the cartoon version of socialism. Capitalism just means that the means of production in a society are owned and controlled by private owners instead of by workers or the government as a proxy for workers. It says nothing about whether people are compelled to be greedy or anti-sharing or something.