I read this post and some thoughts came to mind...
I am under the impression that Eddie is constantly afraid to come truly close with people. It makes total sense, considering his relationship with his parents, the way he was probably raised and considering the last person he let himself connect with, Shannon, died; right after he left him alone once again.
He said it in therapy, he doesn't allow himself to feel emotions. Real closeness creates so many emotions (both positive and negative), that Eddie is not ready for yet. He obviously suffers from ptsd, which has definitely been reactivated after the shooting in 4x14. He craves closeness, both physical and emotional but he is still terrified of it.
We can obviously see his hesitance and restrain with Ana. It looks like he is trying to relax and give in but can't; not completely.
It is so easy with Buck on the other hand. He trusts him completely (he literally gave him his son in case something happens to him! Still not over that btw), he loves him and can be himself around him. He feels that Buck accepts him for who he is, no conditions.
But still, he keeps himself from going really close.
Christopher? Yes, he can be as close to Buck as he wants. Eddie encourages that every chance he gets.
But himself? No. It's not that simple.
Maybe he is afraid that if they come too close, he will lose Buck too...
(I may be projecting too much here, but these are my thoughts. I love Eddie so much, he needs a hug asap 😭)