It is VERY natural to have the response you are having.
For many people in therapy, the act of opening up to another human is risky business. If you want that person to actually trust or rely on that other person, that can add a whole new level of complication.
Many people in therapy have had to fight their whole lives to stay safe. A large part of that is the struggle to be able to survive on your own. We HAD to not rely on those in authority. We had to do it ourselves. So asking us to trust someone else and rely on them goes against everything we learned the hard way.