I also have an anxious attachment style. My T and I had a discussion about what's in your second paragraph a couple weeks ago. He was talking about not trying to teach me to fly (like a baby bird) or throwing me in the deep end of the pool before he knows I'm ready. I was distressed by this, because what if *I* didn't think I was ready? He said it was based on what I think I need/am ready for, not what he thinks I need/am ready for. That at some point, ideally, I just won't feel the same dependence, that I might not even want to email him if I'm feeling bad, that I'd reach out to other people and/or manage on my own. And I'm not at that point yet. Essentially, it would ultimately be me who pulls away rather than his pushing me away/pulling back. That made me feel much better.
So that could be something to talk to your T about, Merope.