This is an interesting subject. I'm having similar issues, and sometimes I think that when in those states of depression/ anxiety (and anger which I have a lot repressed) I just don't let people close. It's almost impossible to feel the caring because I'm waliking around with a "go away you can't understand me anyway" note on my forehead. In the same time I hope they will come and stay with me and listen and understand.
I'm not sure logic works when in high anxiety mode. Maybe what helps is to be aware that we are in a very reactive mode where we push people away because it is more possible for them to hurt us then to help us.