Everyone exhibits behaviors, sometimes traits, that go with all the "disorders", we're all human and subject to all the emotions and susceptibilities. We can't get into each other's experiences though so, looking from the outside, we can't know exactly what moves a person to do this or that activity. One person might isolate because they're depressed, another because they're anxious and a third for both reasons.

Behavior is too complex to fit others into convenient pigeon holes but that does not mean the classifications are useless. The classifications are for professionals so they can get a better idea how or where to start treating a person who comes to them for help. Some individuals like knowing how they are classified by the professionals they are working with.

A professional that uses a classification system in their work is going to use it to classify and often, that means all whom they come in contact with. It is partially how they "think" and perceive their world. If your therapist, from your description of your parents acts, felt your parents had traits of personality disorders, s/he probably has a reason for telling you, you should discuss it with him/her. It is not right or wrong, true or false, it's just a schema some use for understanding their world better. If you do not find it useful for you, then it is not useful for you. But to understand what another is saying/doing you have to talk to that other about it as anyone else's opinion would only be a guess.