White Americans or European Americans are the same thing and they are an ethnic group. Do you need a dictionary.com definition of an ethnic group? It sounds like you do.

eth·nic·i·ty eTH'nis?de/ noun the fact or state of belonging to a social group that has a common national or cultural tradition.

Explain to me how white american doesn't qualify as an ethnicity. The fact that it is thoughtcrime to identify with one another as an ethnicity should raise some red flags for you.