Set me thinking - perhaps all animals or all life forms even should be banned! The world really would be a safer place then.
Dogs carry Nesporosis -causes cattle to abort
Badgers (according to farmers) carry TBC
Mice and rats propogate all manner of ills including some recent cases of Bubonic plague in the US
Cows can give you BSE through their meat
Chicken and eggs cause frequent Salmonella outbreaks
Rabbits carry Myxomatosis
Birds - avian flu just for starters
Pigs -swine flu etc
Mosquitos carry Malaria
Pigeons carry, among many other things, Cryptococcosis which is a potentially fatal respiratory illness which affects cattle and humans.
Humans -now lets get to them, all manner of ills they carry and share among themselves - 80% of all known sufferers of the nasty disease that pigeons carry, which I mentioned above, have AIDS - should we ban them too?
Or maybe they
could all just walk round with a little bell to keep other people away...or failing that ...
Unfortunately the weaker members of any population are open to attack from many pathogens carried by many different vectors (The vectors are not all living things eg the air we breathe). It's natures way of keeping things balanced on the planet -ever heard of a theory called natural selection?
Start by reading about Charles Darwin , then maybe you could continue to research Richard Dawkin's splendid book The Blind Watchmaker...
If you are relatively fit and healthy you should be OK to keep cats as a pet so don't worry and for the weaker members of the human race fortunately there are modern medicines and vaccinations to help them in the fight for survival.