I think you're making a lot of assumptions about your therapist.

People in marriages, for example, can still experience deep loneliness.

To some extent, we are all trapped in our own bodies and minds and can never truly "know" another person.

My therapist is very different than me. He's a man. He's much older. Still, I think he "gets" me on some deep level. I wonder if the issue is the general facts of your therapist's life or whether you just are not clicking.

I also wonder, though, if your feeling of a barrier is one you are constructing yourself--if you have something invested in not being known or feel afraid to be known. It's just something to think about.