Just had that conversation with our neighbor a few weeks ago. Somebody dumped a rooster and hen at his place, she now has chicks. He tell's me "Oh your chickens look so comfortable and happy, you have a nice set up for them, how about I just bring you over a few more?" Umm, no! I sure don't need more roosters and I don't want strange birds from who knows where. Not to mention the hassle of introducing a new hen. Just not interested right now.
Then of course there's all the dogs and kittens. I just have to send them all to the shelter so why can't they?! Why does everybody think that because I have dogs and cats I should take all theirs too when they get tired of it?! Especially the jerks that dumped the tiny black kitten here last November. Freezing cold, rainy night. Sweet friendly thing, skin and bones, shivering in the cold, broke my heart to see her. She snuggled right into my jacket, purring up a storm, and now I have 6 cats instead of 5!