TL;DR Varric's so afraid he'll be like his parents- that he'll be stuck in the past like they were- that he basically has become them. He can't let go of Bianca because they were SO good together. It was such a good time in his life, letting go of it is too much. He doesn't even seem to know he's clinging the way he is and clearly as the inquisitor, we're not nearly good enough friends to call him out on this. Man I wish Hawke was able to >.>
I don't want to dislike Bianca, I want her to be as great as Varric says. I mean I really like her being a great smith is boss and she's clearly smart even though she clearly suffers from a case of Mary Sue syndrome. Anyway as much as we dislike Bianca for what she's been up to in this relationship, Varric is just as much to blame for clinging to the past as he has been.
Which really only makes this all the more saddening. If this was meant to further his character, all we get out of this is an understanding of Varric's layers. Varric is kind and compassionate, he's clever and stubborn, funny and creative, he tends to hold grudges (like he did when his brother trapped him in the deep roads). But we know now that there is a facet of Varric that is very sad to accept. He clings to people even if they aren't good for him anymore because of who they were to him.
It's sadder still because when you compare this to Cole's friendship quest- Varric can so easily see that Cole needs to grow to move on. And yet, Varric can't see that for himself. Maybe it's because Varric has this issue that he can empathize with people so easily and tries to help.
I basically have to resign myself to knowing that this is cannon Varric now, whether I like it or not. And I can respect that his is what the writers wanted, that Varric is much more complex than we thought (even if it hurts to see). I just REALLY hope that there isn't some DLC that suddenly, without any real change in either character, gets Bianca and Varric back together because it was "twu luv" after all. I'd much prefer to see Varric finally lay it all to rest. And I'm not saying that because I want him to be a LI in some other game. I just want this character to be happy and healthy. Right now, he's not really either and it breaks my heart.