Anti-logic

On Saturday, my next door neighbor knocks on my door - rather loudly, I must add. I just moved into the building a few weeks ago and so far was on friendly terms with their rather large family. So I open the door and smile.
"Your cat poops on my doormat" - she says without the preliminaries.
"I am sorry, but it is impossible," I answer, still smiling. "Our door is never open for the cat to get out; besides, she is scared to go out of the door".
I omitted the fact that the sheer amount of cat poop I find inside my house leaves none to be deposited outside.
"I have seen various stray cats inside the building. I am sure it's one of them," I add.
"It never happened before you moved here," insists the neighbor. "It must be your cat."
"But my cat doesn't go out!"

After 10 minutes of this exchange, still unconvinced, she turns to go back inside.
"I am going to put some poison out. Don't blame me if your cat dies" is her parting shot.

Poor street cats!