Yes, race and gender are social constructs. But what, other than a spectrum of skin tones, defines one "race" vs another? If I want to be Chinese what would that mean? I can live culturally similar, very similar if not exactly the same, as any Chinese person. And while there are many people with Chinese heritage and/or people who came to the U.S. from China, they can live and act in many different ways, they can become completely "Americanized." Those who are a few generations deep in the U.S. I'm sure share little cultural identity with mainland Chinese people.
So if I say I'm Chinese as a race, what happens next? Being that race doesn't tie me to any particular cultural behaviours because people who are from China are not bound to Chinese culture.