This is an old bug and I'm supriced no one mentioned it before.

Basically ALL pets will try to follow the player if the player is being attacked, even if they were sitting down, they will stand up and go close to the player and do nothing, when the hostile mob(s) die they will sit where they are at that moment.

This could make sense with the dogs because they can actually help attacking enemy mobs (tho, is still a little annoying by the fact that they can easily die), but what in the world are the parrots and cats thinking then? They are risking their lives for no reason!!

Please fix this bug, I got scared of loosing my pets due to this everytime I'm fighting too close of my house.