Why he won't look at me?

Writing out the whole story would be too long, so I will summarize it here. I want you generous guys who spend time to read this post to share your guess: why he won't look at me?

Our story:
We have two little kids together. We divorced two years ago. It was a nasty one. He was not fair during the divorce and he knows it. He has been very accommodating to my life, probably partially guilt-driven. (I of course don't take advantage of this aspect. Gratitude is all I have about this, despite that he was not fair to begin with.) A few months ago, I asked him to consider getting back together and he said no. At some point after that, things changed. He told me he realized what he did that made our relationship not working, but he also said he has not made meaningful improvements. Shortly after that, we started having dinner regularly at his place - with kids, spending weekends together - with kids. He greets me online. He seems warm online. But when we meet in person, he avoids eye contact with me often. In the most recent encounter, he was super tense around me, until I broke the silence to talk, then we made plans to go out tomorrow together and to have dinner together. He has also told me he is attracted to me, and said he doesn't think that will ever change. I also think he has unresolved hurt feelings. He was doing readings regularly related to relationship - last time I know that happened was a few months ago, the same time he said he figured out his part of contribution to the failing of our relationship.

Any thoughts why he won't look at me?

can he be ashamed?