I thought garlic was a member of the onion family and grew in the garden.

Oh, it is. Buuut, in a way similar to how onions and garlic were considered aphrodisiacs by the ancient Romans, they're treated as heating food by Hindu culinary traditions, and therefore categorised with meat. It makes a certain sort of sense when you remember that pure vegetarian dishes were recommended for people who for various reasons weren't supposed to get their blood and libido up and running: mendicants, widows, etc.