It's such a simple explanation for our stalemate, but it's so accurate. Ultimately, I don't want to force him to do something that he doesn't desire, because I want him to be happy. He doesn't want to deny me something I desire because he wants me to be happy. We are at odds because we both have strong opposing desires, and yet we both want to make big life decisions so that the other is happy.
Of course it works the other way too- I am used to him seeing that something is really important to me, to my happiness, and giving in. When he refused to budge on this, it made me so angry at him. And just angry at the situation in general because I honestly don't want to force his hand, to compromise his happiness. He is in the same situation- or the opposite situation, depending how you look at it- with me.
This aspect- this honest desire that the other one is happy- is what is so heartbreaking about not being able to reach a mutually pleasing decision. As someone said in the comments, there is no compromise- you can't have half of a child- it's either CHILD or NO CHILD. And it's either get what I want and make him unhappy or give him what he wants and be unhappy myself.
(Note that I do not see myself as responsible for his happiness- he's responsible for that and vice versa, of course. It's just that when decisions can be made that we know will make the other happy, we are motivated to do so.)