When you hit another mob it will attack it so, that would most likely not be a glitch.

No, it is a glitch. Tamed mobs should not attack each other.

I think it's not a glitch or it is just a glitch for the same animal so yeah

No its not a glitch the Cockatrice will killed tamed mobs so don't hit them get the friendly fire mod,

Btw its been like this sense they added them, So I mean how did you not notice?