Well, in my case I have an anaphylactic reaction to cats, including dander, fur, oils, etc, so having them in the closed-circulation cabin air could indeed be fatal.
It's especially worrisome since allergic reactions often intensify the more often they occur -- someone might not even realize that the next one could be fatal until it's 2 hours too late into a 5+ hour flight.
"Call immediately. Time is running out. We both need to do something monstrous before we die." -- Message from Ralph Steadman to Hunter Thompson