Nate is doing this, primarily, because the only family he ever had, for most of his life, Sam, suddenly reappears and is in dire need of his help...or at least he has every reason to believe that's the situation. Elena seems to just dismiss Sam out of hand even when she meets him. You'd think she'd be somewhat more forgiving since a brother he thought was dead for 15 years is actually alive, and in trouble. But no, because he lied to her, she's dead set on punishing him for that betrayal. Never mind what good intentions he may have had in mind.
Maybe there's more of a schism between how Elena reacts, and how I would think she should react because, we, as the players get to see what Nate and Sam's interactions were like as kids from the very beginning of the game. We know that they had each others' backs, no matter what, when they were growing up. So when Elena can't do the same, because Nate lied to her, to protect their relationship (as he explains later in the game), just felt generic and unrelatable to me.
Sure, Nate and Elena slowly regain their passion for each other toward the end of the game as they reprise the glory days they had in Uncharted 1, but by then the game had spent hours and hours as they snapped at each other, and as Elena was there to pull Drake back down to Earth every time he showed any type of enthusiasm for the treasure hunt.