OTOH, there's the curious case that JoeMorgue makes, viz., that the actually available size under the seats is smaller than the size limits that United posts on their website. So, it could be that the kennel the owner brought adhered to the requirements, but still stuck out into the aisle.
No, to be clear I'm not saying that the size limits United has on their website are wrong. I'm saying the size limits as posted on their website even if accurate are far to small to fit even a toy dog in a soft sided carrier under.
Which is why I found the whole "Oh have you ever flown?" snark I got so unnecessary. I've flown dozens of times and never once encountered a seat far enough off the floor of the plane to have enough space for pet storage.
In which case, they should have been allowed boarding and different arrangements made for the pet carrier.
What "different arrangement?" Can't go under the seat, can't go in the aisle, can't go in a seat, can't go in the overhead.
As long as the airlines pretend that "under seat storage" is a viable option for anything larger than a sheet of graphene the ground level (no pun) flight crews are going to be forced into no-win situations.