There doesn't seem to be an established term "be pet" with a specific etymology. "Pet" is a noun that refers to a domesticated animal kept for companionship or pleasure. However, if you are referring to the phrase "be a pet" or "be someone's pet", it typically means to be someone's favorite, to be treated with favoritism or indulgence. In this case, the word "pet" is used metaphorically, comparing someone to a beloved animal that is kept and cared for.