I don't think I've ever been advised that, as an asthmatic from childhood with persistent rhinitis. Not that I would pay any attention to so absurd a suggestion, so it's possible that it's been said to me and I've rudely laughed in the person's face and as a result had some sort of note put on my permanent record...

I have every sympathy with people who have genuine serious allergies to other mammalian species, or for that matter, people who have genuine fears that they find it hard to conquer, but people who go 'oh, I have asthma, the cat must go' without investigating the matter properly, I have no time for them.

Apologies, pet rant triggered...