It's hard to over-state the importance of these little humanizing details, but it's the fundamental difference between this film and Marvel-Disney's recent offerings, which are as charming as they are profoundly formulaic: they're good like junk food is good, like cake is good, like anything is good that lets you forget about how bad things are sometimes.
The Amazing Spider-Man doesn't shy away from those complications, but delves into them—but only sometimes. Consider the age-old superhero dilemma: I Can't Be With You Because It Will Put Your Life In Danger (Superman/Batman/Iron Man/Spider-Man says, frowning). When Peter says that quote almost word-for-word in this film, Gwen shoots back: "You want to break up… so that you don't lose me? Who does that work out for?" It's not as clean-cut or morally concise as it usually seems in films like this—and that's because Spider-Man seems to want to vehemently resist being grouped in with Disney-Marvel's "Films like this" genre of superhero movies.
But much like its titular character, The Amazing Spider-Man 2 has commitment issues—specifically, with sticking to trying to be "alternative." Consider Dane DeHaan's character, Norman Osbourne's Harry—shipped off to boarding school at a young age and neglected all his life. Early scenes give DeHaan an ability to showcase what made his breakout performance in Chronicle so captivating—a friendliness and genuine warmth that coexist with deep bitterness and pain. However, barely two scenes pass before the friendliness and warmth in his character get tied to cinder blocks and thrown into the Hudson, and DeHaan becomes just another cackling menace for Spidey to take down.
By the time the film's 140 minutes are up, it seems clear that Webb doesn't want to make a superhero movie. Perhaps out of spite, when he does do the obligatory Superhero Stuff, he populates it with the most hackneyed, cliched, stilted stuff available. This is why the excellent chemistry mentioned supra is such a bummer—Webb is clearly annoyed by superhero conventions, but uses them anyway.
As for Gwen's line quoted above, it doesn't stop her and Peter from breaking up, then un-breaking up, just like we all expected. In most cases, Webb cedes to the Way Things Are Done, going with the flow while making it clear he wishes he weren't.
And for all the expensive CGI, the lovingly-rendered flapping of Spidey's suit as he plummets face-first toward Sixth Avenue, The Amazing Spider-Man 2 is at its best when it's low to the ground—Peter talking to Harry, Harry talking to Gwen, Peter and Gwen flirting, etc. There's a reason the writers over at Disney-Marvel—who are, by the way, absolute master technicians—keep the interpersonal relations so insubstantial in their movies, so surface level, so consistently witty and quick, as if everyone in the Avengers had relocated from Stars Hollow: it helps us forget how empty all the blowing-stuff-up is. The action in The Amazing Spider-Man 2 is exciting, white-knuckling, heart-pounding, whatever—but it's not 1/10th as real as a single awkward flirtatious conversation, or a rekindled friendship, or the loss of someone you love. It's unfortunate that Webb insisted on injecting the film with the interactions of a much better film—it makes all the web-slinging seem bland at best.