The title explains it all.
My dog would most likely be a Titan defender he is strong/ defends thing
My cat would be a blade dancer he is the spawn of oryx and wants to kill everything in the galaxy.
EDIT a pet in real life or irl and what class/subclass would your pet be and why
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Two boa constrictors - probably Defender Titans, put them in a bubble (their hides) and they just sit there. For days