What false scientific theory did the nazis use to justify their persecution of jews

It would be the idea of a future society that only the Aryan race and the race that they think is superior can lived in such society. This is called as the Selective Breeding by the Nazi scientists that support the ideology of superiority of the German people and other races are inferior or they would not even consider them as men.

Phrenology-- pseudoscience based on the shape and structure of the skull

The study of phrenology is based on the concept that the skull demonstrates evolutionary differences between races and people. The Nazis used the theory to "prove" the superiority of the Aryan race. The bumps and contour of the skull was believed to show evolutionary superiority or weakness of the races. this theory is more commonly known as "racial science".