I seem to only like my own pet...

I don't think that is necessarily a super weird thing. My friend is the same way. She adores her little pug but is awkward around other people's dogs. I suppose it's similar to loving your own children but being annoyed by someone else's. My friend takes her dog for long walks but purposely avoids dog parks so she can avoid running into other people's dogs in large numbers.

It's funny, her doggy sheds like crazy but she can't stand other dogs fur.