Cats or dogs is the oldest icebreaker there is, and it still works because almost nobody answers it slowly. People have a side before they have a reason, which is exactly what you want for warming up a quiet room. Put two slices on a wheel, spin it where everyone can see, and the group has a topic, a verdict, and something to shout about within about eight seconds.
The two answers stand for different lives, which is why the argument runs hot. Cats mean coming home to an animal that is pleased in its own understated way, a small flat that works fine, and quiet evenings. Dogs mean a walk at seven in the rain, a reason to leave the house, and company that never once plays it cool. Plenty of people are honestly both.
Used as a prompt, the best trick is to let the spin assign the side rather than reveal it, so whoever spins has to argue whatever came up. If you are genuinely choosing a pet, treat this as a way to start the conversation and nothing more, because hours, space, allergies, cost, and who does the walking are what decide that. The draw itself is an even chance each, from your browser's cryptographically secure random generator.