Why do Americans still believe in the science-debunked "race theory" categorizing humans like dog breeds, but Europeans don't?

Why do forensic scientists still classify people by race? 😁

I'm not sure what you mean by debunked. There are markers that you can point to for different races, which is why you can get DNA profiles that tell you how much of each you are.

they are like dog breeds

I thought we were all 'human'.

you're just mad because you're an inferior mexican.

US politicians have found race (also gender, ethnicity, religion and sexual orientation) a convenient way to divide and conquer the electorate. Employing identity politics has proved a good way to distract people from questioning the actual policies (or lack of) of a given politician or party. It may interest you to know that Americans are so disgusted by the two-party system that more eligible voters stay home than actually cast ballots in these farces we call elections.

Some Americans are just dumb, most know we are all one race biologically.

There are no hard-fast rules in defining races, they can be defined by religion, national-origin, culture, common physical characteristics etc. There is no reliable or consistent biological categories. Arabs, Persians, Mexicans, Jews, Muslims, Italians, Irish Catholics, blacks can all, and have all been called another race. Discrimination against any group based on this fluid definition can be called racism. 

again 

Race is a concept used in the categorization of humans into groups, called races or racial groups, based on combinations of shared physical traits, ancestry, genetics, and social or cultural traits. Although such groupings lack a firm basis in modern biology, they continue to have a strong influence over contemporary social relations.

https://en.wikipedia.org/wiki/Race_(human_categorization)

The human species has no subspecies, because all major populations are genetically mixed, and have been so for centuries. In the human species there has been a substantial amount of "RACE-MIXING", therefore it would not be correct to speak of human "subspecieses". Most Whites have a fair amount of "Black" and "Asian" blood, most Blacks have a certain amount of "White" or "Asian" blood, therefore it would not be appropriate to speak of "White Race" or "Black Race" or "Asian Race". Race Mixing has become a HALLMARK, a distinguishing feature of the human species, which sets us apart from other species.

Pbs

DNA

https://www.pbs.org/newshour/show/the-ancient-dna-revolution-unlocks-how-connected-we-all-are

I think the dog-human comparison is a good one. Dogs are the descendants of wolves that through human interference diverged into various breeds. No one questions that humans went through similar but slower evolution. Humans do not say different breeds of dogs are a separate dog race. My wife is Asian, not a different race.

Because in the U.S. racism is baked into the cake, here from the beginning, never admitted and never reconciled.