Many of us fear needing someone else because we haven't had good experiences with that in the past. Maybe people let us down, or left our lives in some way, leaving us to grieve the loss. That can be really painful. Being completely self-sufficient is a way to not let people hurt us. But it can hurt you just as much as being completely dependent can subsume you.

I used to say that I was fiercely independent. T says I've put emphasis on the "fierce." In order to keep people from hurting me by letting me down, I haven't given them the chance to help me.

No one can be completely independent. But there is a happy medium between being completely independent (and therefore mostly alone) and being completely dependent (and therefore losing yourself). Interdependence is a good way to think of it. There's no better relationship in which to develop those interdependency skills that with your therapist. Yes, at some point the relationship will end. But by the time it does, you will have developed the skills to get what you need from others outside of the therapy relationship. Moving on from your T is not something to fear - indeed, it's really the ultimate goal for anyone in therapy.

On a side note, my T has told me repeatedly that calling him between sessions for a crisis actually helps him. If I call him right at the start of an issue, he can help me work through it, but if I wait a long time, it can seem so big that it takes him a lot more work to help me through it. It's his sneaky way of using my desire to not be a burden to get me to do something that I consider being a burden.