In case you're serious with the sphinx question: in ancient Greek myth the entrance to the city of Thebes was guarded by a sphinx who would only let you through if you could solve a riddle, otherwise the sphinx would eat you. Which riddle that would be changes from story to story but the most famous one is along the lines of "What creature walks on four legs in the morning, two at noon and three in the evening?". This was eventually solved by king Oedipus who realized it was a human who crawls as a baby, walks on two legs as an adult and needs a walking stick as a third leg when they're old. Depending on which version you read, the sphinx was either so shocked by him solving the riddle that it threw itself from a cliff or was simply slain by him.
“What creature walks on four legs in the morning, two at noon and three in the evening?”
Traveler: Me, when I wake up with a hangover in the morning, sober up by noon, then get so much withdrawal that I need a walking cane on my way to the bar again in the evening.
Depending on which version you read, the sphinx was either so shocked by him solving the riddle that it threw itself from a cliff or was simply slain by him
omg this part I did not know. I just thought it...let him pass.
But anyway, what does that have to do with the "pun battle" as posed in this story?
Well, you could consider the solution to the riddle a pun though that's quite a stretch. Though there is at least one modern rendition (in German) that directly uses a more pun-ny solution. It does't quite translate to English but I'll try. Basically, Oedipus thinks and thinks until he starts to complain "Ach Mensch..." which is roughly equal to English "Oh boy..." but "Mensch" is literally the German for "human" so it's the right solution and the sphinx has to accept it. If you understand German, I highly recommend checking out this version. It's "König Ödipus" by Bodo Wartke. He plays all roles himself on a mostly empty stage with only a couple of props and it's absolutely hilarious. The sphinx is a lion hand puppet.
“What creature walks on four legs in the morning, two at noon and three in the evening?”
A kobold. In the morning it scurries around on all fours, trying to get everything in order before its master wakes up. At midday, it stands at attention before its master. By the evening, it gets tired and leans on its tail a bit.
Way less gross. Human and centaur are both intelligent, can communicate, and give consent, so it would be fine. With a horse (which has none of these things) the centaur would be committing bestiality.
Apply the Harkness test (self aware intelligence, physical maturity, and ability to communicate consent). Both humans and centaurs pass assuming the individual is a willing adult, horses fail twice due to being nonsapient and uncommunicative.
From the human perpective, probably the horse is a little bit less gross. From the centaur perpective, probably the human is less gross, but I’m only half centaur, so can’t speak for all of them.