Therapists are trained and paid to set aside their own needs for an hour and focus everything on YOU.

Also remember that most therapists have seen hundreds of patients (even in the context of their graduate school training) so they have probably heard a variation of everything before. There is very little that can offend them/shock them even though they are human.

Their training allows them to empathize with a patient without taking things personally. Moreover, most therapist's see patients back to back. So even though once you leave their office you are thinking about the session, their whole attention is now focused on another patient.

It makes complete sense that you would be worried about their feelings, but you are paying for the service of NOT having to consider their feelings.