Someone could be allergic to cats. That’s a pretty good reason to not allow them in the cabin.
seat would be allotted accordingly in such cases.
Because people can be allergic to cats, dogs, many other animals or various other things too.
That does not mean that for 1 passenger, another passenger would not board the flight, or leave the pet at the very last moment (because while we book a sit and have a pet, it is advised to call up and buy the ticket, because firstly such a seat would be allotted to that passenger where there is good leg space, secondly there is a restriction to a number of pets allowed in cabin in a flight).
I think it is a very common scenario that someone can be allergic to pets and some flight companies still allows pets on cabin.
There are various rules and restrictions and procedures to take pets on flight and if followed, they would not deny to take the pet in.
Lastly, I and my husband called up various airlines to enquiry about travelling with pet and trust me none told us or shared with us any documents which says about people being allergic to certain animals