Why would a toxic person annoy/irritate someone (of the same gender) on purpose? Are they not happy with themselves?

I’m guessing so, or jealous.

Think it's more of a childish way to get attention or as a way to assert their false power over others. They enjoy getting a reaction.

I truly believe this, especially if they follow and criticize your every move. Quite sad...

Bully?

Nope ... it'll be more sinister than that, they see you as being happy, but instead of them trying to emulate you {too much hard work for them} they try and bring you down to their level