I very purposely didn't say "more" ... I said "first" -- I also don't think the MC loves any of the girls he loves* more than the others. I DEFINITELY don't think he loves his daughters less than his wife.
BUT Anna is his glue. Anna is his muse. Anna is his constant. Anna is his enabler. Anna is his everything. Also, CLEARLY Anna is as connected to him as he is to his twin (and she has been since they first met), just in a different way.
I also reject your statement that the other characters think the MC did something wrong, or that he ran away from Jessica because she gave him an ultimatum. The other characters don't even know exactly what their beef is, and for the most part they assume it's just something to do with Jessica Being Jessica™. Shoot, Anna DOES know what the cause is and she doesn't blame the MC, she blames herself.
I don't know if you're not far enough into the story, or you're misinterpreting things, but while Jessica was upset when the MC and Anna moved from their home town (shoot, she was upset that he got married in the first place, she was just less obvious about why back then), she didn't drop her ultimatum until after the kids were born and Anna basically told the MC that he should try and bring Jessica into the fold (as it were) because she thought it would make Jessica finally happy. Needless to say, she may have been a bit premature ...
And her ultimatum wasn't "Don't leave me" ... that was just what she wanted. Her ultimatum was "I want you to myself, and you'll break me if you don't leave everyone else behind for me." ... and on a VERY TINY level it is his and Anna's fault that she was brought to that moment, but it is ENTIRELY her fault that she went through with the ultimatum ... and from everything we've seen, she beats herself up over it all the time, leading to much of her continued erratic behavior.
So yes, while Anna in particular, and the others in subjective theory, think the MC can "fix" things eventually, it's not because they think he's to blame for something, it's because they believe in the MC. They believe that he's as good a person as they'll ever meet, and if ANYONE can get through to Jessica and heal whatever rift is between them, it's him.
*On a side note, I think this is my issue with Lisa, and makes me wonder about some of his "permissions" that his wife was giving him. Every other character he is involved with he "loves" and are family. Every other character he will potentially be involved with (at least for now) is someone he clearly loves and are at least LIKE family. Lisa doesn't fit ... in a way, she feels more like a MNF "friend with benefits" character than a MNM character. I suspect there will be more of these people (the first library girl comes to mind) but I hope most will be more like Samantha, Sabine, Valeria, Alba, etc.
Thank you for coming to my TED talk ...