Yes. For example, if everyone were extremely greedy and vengeful everyone could fight each other over wealth all the time and not like each other, not because of personality differences, but because of personality similarities. I guess if there were zero other people, the one person could just respond with psychosis and making up an imaginary dating partner and no one would be able to call them out, though.
I'm still not convinced it's possible to dislike everyone else who exists. It may not be up to you.