Wawrzyn, over time it is likely that your therapist will come to care about you deeply as a human being. In order for therapy to be effective, however, it is inappropriate for your therapist to care about you as a 'friend'. Friends don't help and support us through the depths of therapeutic work - therapists do.
That is by no means settling for something 'less'. The therapeutic relationship has the potential to be far more powerful and transformative than the bond between friends can be.

I have bumped into my T outside the office on several occasions. She acknowledged me, happily, but only after I initiated the interaction with her. She later told me that she doesn't acknowledge clients outside the office unless they do to her first, for the same reason others have stated here - confidentiality.
This is an important rule that most therapists abide by. It has nothing to do with caring or not caring about a client, and everything to do with protecting client confidentiality - which is vital for effective therapy. A therapist who breaks confidentiality (except where legally required) is worth diddly squat.