I think Steve is terrified that his happiness will somehow lead to disaster - there's couple of pages at the end of "Reborn" where he's thinking of the future he saw, which started with him settling down with Sharon, having kids, and having a happy life, but that put in motion events that lead to catastrophe for the world. He's the leader, he's the strategist, but what if he blows it? What if he's wrong? What if he chooses himself and his wish for a stable life and a family, and it turns out to be a terrible mistake?

As for Tony, he's likely frightened that loving someone will lead to their death. He loved Rumiko and she was murdered in front of him...he loved Happy as a brother and he died protecting Tony...he loved Steve and he was assassinated....