Do you have to work with people to be a Psychologist?

The type of psychologist that your parents are thinking of is a clinical psychologist, however there are many other types of psychologists, and their jobs involve research, not direct human interventions. You should show them that the APA has 53 distinct divisions, including industrial/organizational psychology, developmental psychology, behavioral neuroscience, health psychology, etc. You're definitely right about psychology being a vast field but for people who aren't aware, they tend to think about it in the stereotypical way that you outlined. In the end, you don't have to work with people to be a psychologist, you just have to be passionate about how complex they are.

To answer your main question - not necessarily. If you do experimental psychology (research), you may have to do very little in terms of "working with people". Also, you could likely dip into forensic psych and not do TOO much work with many people.

The idea your parents have of psychology is VERY inaccurate, and is only one very slight aspect of the field (counseling), as I'm sure you know. Do what you want to do, study psych if you feel the calling, and SHOW them through your career choice that there IS more to psych than stereotypical crap you see on TV!!!

Nothing. They should support and encourage you. Who cares what they think? At least you are IN college! Do what you want, because it is better to be passionate about what you do. You have to work with people in almost every job. Whether the are co-workers, or clients is another story. You could also TEACH psychology