Your cat tells me a different story, and cats can't lie.
A stray cat wouldn't have called out to you as you walked out the door. I'm surprised your cat's piteous little peep didn't break your heart like it did mine.
Ordinarily stray cats don't allow strangers to pick them up and comfort them. But your cat did, nestling its nose in the crook of my arm as if to block out the sight of the cage that will be its home.
Another thing stray cats don't do is roll over on their backs while they're being cuddled. When your cat was a kitten, someone, perhaps you, carried it around like a baby.
So, tell me you're broke, and you can't afford cat food. Tell me your landlord doesn't allow animals and threatened to throw you out in the streets. Tell me your neighbors moved out in the middle of the night and left their cat behind. Tell me your cat doesn't go with your new couch. But please, don't tell me your cat's a stray.