It is so reasonable I can't fathom it.
Among the reasons cited for the new rules is a dramatic surge in on-board incidents involving the animals.
Those include urination and defecation, as well as people being bitten and barked and growled at.
There's something rather unique about aeroplane rage — the anger with which some people react when the person in front of them reclines their seat is beyond what would be considered normal on solid ground.
Give those same people incidents of animal urination and defecation to deal with and you're pushing things beyond any tolerable level.
I may not be a paid-up member of the pet appreciation society, but I don't think I'm alone in not wanting Ignatius the iguana as a seat-mate.
But beyond passengers generally not wanting to travel in some sort of flying Noah's Ark, surely there are also some major animal welfare issues to take into account here?
A number of airlines reassessed their policies for comfort animals following an incident in January when a peacock was refused entry to a United Airlines flight. (Yes, that actually happened.)
I'm no peacock whisperer, but I don't think it's going out on a limb to say that four hours inside a small aeroplane cabin isn't a great day for these birds and that they probably wouldn't enjoy the experience.
Also in a case this year a dog died after a flight attendant told the owner to put it in an overhead storage compartment.
United Airlines says the number of people wanting to take pets along on flights has risen 75 per cent in a year — that's 76,000 people on just one airline who feel they need to take a furry friend along for the journey.
Among the genuine requests have been passengers who wanted to bring along a kangaroo, a turkey, possums, snakes and a duck named Mr Stinkerbutt.
Is it a novelty thing? A bizarre kind of adult show-and-tell in which you try to bring the most insane creature possible? Are people trying to one-up each other?
Or are there seriously people who feel that having Mr Tibbles the turtle there will make everything okay?
I appreciate that flying is a huge stress for many but if that's what you need to make the trip work, you're going to need to find another mode of transport.
As you'd expect, American Airlines has gone out of its way to prove that it is sensitive to the needs of its customers.
It consulted extensively with groups representing people with disabilities before announcing the ban, and the press communications included a video interview with the My Blind Spot CEO discussing the genuine need for service animals.
But actually, I'd really like to see someone call out those passengers who argue that having Romelda the Rabbit with them on their flight is a medical need.
More often than not it's probably a scam to avoid paying fees to transport pets — and it feels like a bit of a slap in the face to people who require service animals to live their lives each day.
