Yes it is sad that most people will not rent out to pet owners.
But honestly i understand why some landlords are so anti pets. I have seen absolutely DISGUSTING apartments that were ruined by the tenants.

People seem to have a lot less respect when they are not the actual owners. And these selfish people ruin it for all the responsible pet owners out there.

If I was renting out an apartment I would probably add extra security deposits for animals too. If the tenant leaves the house in more of less the same state as they entered it, the money would be returned, no problem.