He doesn't pull away, and he goes with her willingly enough. She seems to know what to do and she actually understands things about him that most others don't, so he opts to lay out the largest of his hesitations.

"He has people. They know what to do." People who are far, far better at delivering comfort. It's not like Max never knew how to care for someone who was sick, so it's not like he's unaware that his reaction every time Eggsy dies makes him kind of an asshole. So he adds reluctantly, "I don't."