Some random thoughts:
1/ Many men–particularly the ones who hang out at bars hoping to meet women–are intimidated by any woman with advanced education or professional status. Women who are lawyers, MBAs and physicians have experiences similiar to yours (except maybe the lawyers get asked for free legal advice, the MBAs are hustled for stock tips, and the physicians have to listen to “doc, i got this pain here in my side…”) If you introduced yourself as, say, the president of a consulting company, a lot of men would still politely excuse themselves.
2/ I have seen shrinks slip into their professonal mode–careful listening, responsive questions–in a variety of social situations, and I think they do it unconsciously. Maybe you don’t actually say “how does that make you feel?” (although I’m not sure you are correct when you say that professionals never use those words), but the tone of the conversation becomes very different from ordinary social banter. In particular, people talking to a shrink either find themselves giving up more information than they get in return, and then may be embarrassed, or they go on guard against giving up too much. They may feel in some sense that they are specimens under a microsope. At the same time, putting on your professional face might make social situations easier for you than talking about the weather, sports, traffic congestion etc.
3/ One strategy might be to avoid the “what do you do” conversation, at least at first. Suppose, when people ask you what do you do, you say something like, “I’ve had a long day. I’d rather talk about what I like to do.” Then you can talk about whatever you like: your weekend plans, the art show you just saw, your last vacation, your training for the Boston marathon, whatever. Then give the other person a chance to talk about whatever he likes. Ask him where he travels, or how he likes to spend his time. The “what do you do” question is really just an awkward attempt to find common ground. But it’s not the only thing there is for two people to talk about.
4/ When you do get around to telling people what you do, there are different ways to present the information. Personally, I think “psychotherapist” sounds less intimidating than “psychologist.” Stereotypically, a psychotherapist helps people; a psychologist studies lab rats, and looks at people the same way. You might try to work your ultimate goal into the conversation: “I’m learning to help autistic children” or just “I’m in school to help people with problems” is less intimidating than “I’m a psychologist. Tell me about yourself.”
In short, I would say give people a chance to talk about something other than their jobs. Most of them will be grateful. And when you talk about what you do for a living, make it clear that you’re off-duty.