I like that you brought up that it was open to interpretation! They give the viewer very little to go on as to what is wrong with the relationship, and while watching the movie I felt as though Ryan Gosling's character was in the wrong, but my girlfriend disagreed and we had a pretty good discussion afterward.
A friend was asking me if she should see it with her boyfriend or not, and it made me think about how seeing this with a significant other and talking about it afterward can probably tell you some pretty valuable and useful things about your respective outlooks on behaviour within romantic relationships.
SPOILER AND INTERPRETATION AHEAD
For my part, I thought the union was doomed to begin with, because Michelle Williams' character seemed never to have really figured out what she wanted out of relationships from the beginning - when she talked about her sexual past, and when we saw her interact with her ex, and when we saw the relationship between her parents, it seemed like she had grown accustomed to being treated pretty roughly by men emotionally - plus, as we see in the scene with her boss, that fear that men only value her for her looks is lurking in the back of her mind, and I think she's afraid that that's all she can ever expect. So when Ryan Gosling's character came along and was really quite kind to her all of a sudden, was willing to throw himself into the relationship wholeheartedly and be quite giving, she saw in him the light of salvation. But she had never really thought through what she actually needed in a partner, and so wasn't really equipped to evaluate whether they were suited to each other in any way - she was just running toward the most love and joy she had been shown in a long time. Plus he had that whole noble troubadour thing going on with the music, and she found him very charming I think because he was an escape from her life of responsibility - med school, caring for her grandmother, being a good daughter to her parents - and he was just so chilled out and not putting pressure on her. So when the baby showed up, he looked like a haven.
But she didn't really know him well yet, and so the fundamental incompatibilities in what they wanted out of life hadn't surfaced yet - she hadn't yet discovered just how much it would disappoint her that she compromised her career goals to keep the child, and how much it would frustrate her that he never grew out of his irresponsible troubadour phase. So he's there trying to recapture the magic of their early relationship which was all carefree and honestly a little superficial - their meeting scene is right out of a romantic comedy, and their dancing on the street scene is so very indie flick, but there are no scenes in which you really feel like they're getting to know each other's minds. And she's just wishing he would grow up and get responsible, having finally discovered that that's something she finds important for herself, and wishing he could act as the grown up sometimes when parenting their daughter. It seemed like she felt she was getting older before her eyes, taking on all this responsibility, while he stayed perpetually silly and youthful (emotionally though not physically) and the gap between them just kept growing wider because he saw staying young as beautiful and she saw it as, well, childish. And his solution to problems is to throw more passion and youth and impetuousness at them, but each time he does that it reminds her more and more of how little they really have in common in terms of fundamental world view. Plus, he has a reckless streak that as a viewer terrified me a little - threatening to jump off the bridge if she didn't tell him her secret comes to mind - and that always made her a little uncomfortable but she also found it cute I think. But he never learned how to control it, nor did he ever learn that it wasn't his greatest weapon and way to solve problems, which is how you get the scene with him drunk at the clinic near the end.
Also, they aren't equipped to examine any of this themselves, because as we see in the scene where she tells him about seeing her ex at the bottle shop, they've just never learned to communicate well and they are both in the habit of sweeping emotionally challenging things under the rug, never to deal with them, allowing them to become sore spots, and because he reacts so volatilely to things in general, she has been repressing talking to him openly because the reactions tend to hurt so much, even if that's just him lashing out in pain because he's just trying to be a good husband and he has no idea what he's ever doing wrong.
END SPOILERS
tl;dr my hobby is analysing other people's relationships, can you tell?
