word usage

"I don't want to meet someone." would be an unusual phrasing. I'd assume if it wasn't a mistake (and you meant someone) that you mean

There is someone that I don't want to meet".

(but you don't want to tell me the name of that person for some reason)

Simlarly "I don't want to meet a person" is a strange phrasing. I'd guess you mean "There is one particular person that I don't want to meet".

Normally, for the sense of "I want to meet zero people" use the "I don't want to meet anyone" expression. Using "someone" is not correct for that meaning.

Now, I've just noticed your question uses "like" not "want". In this case you should not use someone nor anyone. What you probably mean is "I don't like to meet new people" or "I don't like making new friends". Neither "someone" nor "anyone" is correct.