Why did the birds get upset by Alice’s talk of her pet, Dinah?

The birds get upset because Dinah likes birds... she likes to catch and eat them.

Alice replied eagerly, for she was always ready to talk about her pet: “Dinah’s our cat. And she’s such a capital one for catching mice you can’t think! And oh, I wish you could see her after the birds! Why, she’ll eat a little bird as soon as look at it!”

This speech caused a remarkable sensation among the party. Some of the birds hurried off at once: one old Magpie began wrapping itself up very carefully, remarking, “I really must be getting home; the night-air doesn’t suit my throat!” and a Canary called out in a trembling voice to its children, “Come away, my dears! It’s high time you were all in bed!” On various pretexts they all moved off, and Alice was soon left alone.