Some US kids CAN add. But they get nowhere in the math field cause of the way our graduate programs are run.
My son graduated Phi Beta Kappa from a top 10 university with both a masters and bachelors degree in theoretical (pure) math, with almost a 4.0 average. He took only very tough academic courses in math and the sciences. He got straight 800's on the GRE (perfect scores). He wanted to get a Ph.D. from a top math school.
His applications to MIT and Berkeley were rejected. Both schools admit almost only foreign students to their math Ph.D. programs. He went to Columbia.
He was one of only two US students entering the math Ph.D. program that year. There were two Russians, two Koreans, two Chinese and one Australian. After the first year the other US student had dropped out.
My son got a second masters. But when he went to take his pre dissertation examination he could not get three faculty members to show up to examine him. They just didn't care. After a year he got burned out and quit. He is now about to graduate from a top five law school and has done quite well there.
US universities have no interest in educating US citizens in mathematics. The way he was treated was extraordinarily shabby. So instead of a top mathemetician which we could use we get another lawyer.
American schools, and Americans in general, do not value theoretical science -- it's not "practical" enough. A lot of Americans see college as a place students should go to get a vocational education -- hamburger flipping and remedial math (so they can give people the correct change), yes -- physics or pure math, no.
When a lot of Americans say they value education, what they really mean at best is that they hope their children will graduate from high school or at least earn a G.E.D., or at worst they want their children to pass the substance-abuse course the judge mandated rather than going to jail.
Our whole system is geared towards the vision educationists had 100 years ago -- provide just enough literacy so that children will grow up to be able to follow simple directions and do repetitive tasks at some factory. Exceptional people can break out of that mold, work hard, and become truly educated. Such people are also considered a threat to the system and, as you found out, they generally do not get much praise or support.
No offense, but there are a lot of reasons why a dedicated research professor will always take an Asian student over an American. The main one being that the Asian will have ZERO social life; the professor knows that the Asian will be in the lab (or working out the details of the profs latest conjecture) 12-15 hours a day...7 days a week.
American education is so devalued that many professors won't take a chance on a native-born.