Why do gardening classes teach how to raise chickens and bees?

No, not usually. You'd need a special bee keeping class or find a bee keeper to teach you. that's how we learned. As for the chicken, we had Mother Earth New magazine and learned from that. Is that still around? I suspect your Cooperative Extension Service for your state may have printed material on the chickens. Or just do a web search on how to care for chickens..........I suspect there's a bunch of info.

A lot of people are raising backyard chickens and have backyard beehives these days. They are very helpful to the maintenance of the environment. Chickens eat bugs, and the bees pollinate the plants. We can't have chickens in our yard, but i did have bees last summer. Unfortunately, the drought here in TX killed them.

Gardening is a part of agriculture, which includes raising all sorts of organisms for food.

Chickens pick the bad bugs, and turned them into fertilizer. Bees increase your yield by pollination, and also give you honey.

Chickens eat bugs, bee's pollinate the crops... they benefit the garden.

Why shouldn't they?

Bees pollinate flowers that grow in gardens.

Many people who have chickens, keep them in their garden.