Well, this is an unusual one - Thomas Jefferson kept a flock of 40-ish sheep on the front lawn of the White House, and one ram in the group was a reeeal asshole. After all, Jefferson actually referred to it only as "this abominable animal." In mid-1808, right near the end of Jefferson's presidency, it attacked a number of people passing through the lawn and actually killed a small boy.
Yes, President Jefferson had a pet ram that murdered a child. He had a murdersheep.
It was eventually transferred to Jefferson's estate of Monticello, where it was killed after killing a few of its fellow rams.
Polly the parrot has one of the best stories ever - owned by the notoriously crass president Andrew Jackson, Polly was the only bird in presidential history to be forcibly removed from a presidential funeral. You see, Jackson had (possibly inadvertently) taught Polly a WHOLE lot of swear words, which Polly would regularly spout off all the time (often when foreign dignitaries were around, who were not a fan of the foulmouthed bird). And then at Jackson's funeral, Polly began swearing like a sailor, and had to be taken away.
Although, something tells me Jackson would have been delighted at the thought of his parrot screeching "FUCK" repeatedly at his funeral.
Teddy Roosevelt might be, objectively-speaking, the coolest president. He's led a pretty crazy life, and one that brought him into constant contact with animals (HE FOUGHT A COUGAR WITH A KNIFE - try to top THAT, literally any other president) and ended up keeping a huge number of pets during his time in the White House, including pigs, rabbits, hyenas, ponies, birds, dogs, and more.
But his best pet was undoubtedly Jonathan Edwards - a black bear given to him sorta as a joke by representatives of West Virginia. After all, it was a freakin' BLACK BEAR - untameable and incredibly dangerous. But Teddy Roosevelt, being freakin' TEDDY ROOSEVELT, tamed it and treated it like a huge dog, more or less - taking it out on walks, feeding it nuts and honey, and even wrestling with it.
But the best part of this black bear owned by the president was its name - JONATHAN EDWARDS. Yes, Teddy Roosevelt gave it a full proper name, in honor of a relative of his long-deceased wife, Edith.
Satan was a dog owned by John Adams - and not much is really known about it, other than it was a dog named Satan who lived in the White House. Honestly, that's enough for me.
John Quincy Adams, in addition to being a "hollow Earth" truther, sounds like a real jackass - he was given an alligator as a gift by a visiting French general, and naturally he decided to leave it in the unfinished East Room of the White House, in a bathtub, with the specific intention of bringing by guests to freak them out.