I know you didn't mean it this way, but the implication that there are "breeds" of people can be very offensive, as it compares someone's lineage to domesticated animals. Racists have long used the term "breed" to describe disenfranchised minority groups in an intentionally derogatory manner. Culture and heritage are baked into our identities, and they are very dear to many people's hearts and vital to our sense of self, which is why you're getting the responses that you are.
It's also not scientifically accurate, because breeds are bred. They are not naturally occurring variations in a species, they are bred for a purpose, by humans, through artificial selection. It's why there are breeds of dogs, cats, and horses, but we don't normally use that word for starfish or rhinos.
Humans don't have breeds because we are not bred with intention in the way that dogs are. We are products of our environment, our culture, and our history. Race is a construct, and the closest thing we have is ethnicity, which is essentially just our ancestry's geographical origins.