Avengers: Endgame - The Devastating Truth Of Why Cap Will Die To Save Tony Stark
3. Captain America: The Man Out Of Time
The key to understanding this theory is Captain America's lost opportunity. He is a man out of time, marked forever by the dance he was supposed to have with Peggy Carter before he heroically sacrificed himself to save the world. His life as it was supposed to be was ripped from him. He's not just a man out of time, in that respect, he's a man out of his own destiny.
Now, Cap is defined by his duty rather than any personal relationships. That's why he pursued justice for Bucky as vehemently as he did: Bucky was his last link to the life that was lost to him.
Constantly in the back of Cap's mind is the destiny he was supposed to live to. He was supposed to go and dance with Peggy. They were supposed to get married, have kids, be conventionally happy. And part of the reason Steve carries Peggy's picture around with him everywhere is not just a token of love, it's one of double-edged loss. The loss of his own life but also the loss of Peggy's.
Because his sacrifice robbed her of her own story too. Sure, she ended up being a keystone of SHIELD and thus a major part in the Avengers Initiative's foundation, but Steve's decision changed at least one major part of the course of her story. The spectre of that decision could ultimately be what drives Cap not only to sacrifice himself for Tony, but what also makes it stick with Stark, overcoming his own obsessions.
And fundamentally, the MCU is very dependable when it comes to these sorts of character developments, so it's fated for something like this to happen.