Neandethal Bones dated 2.5 mya

Neanderthals first appeared about 200k years. Their most immediate ancestors were *probably* Homo heidelbergensis whose earliest appearance was 800k years ago. A genetic estimate shows that Homo sapiens and Homo neanderthalensis diverged from their common ancestor (possibly Homo antecessor, whatever that turns out to be) about 500-600k years ago. So before that, there's no way that there could be a Homo neanderthalensis.At 2.5 million years ago, you have a mix Australopithecines, the earliest Homo habilis and maybe some Paranthropuses but they were all hanging around Africa. As far as we know the first of our ancestors did not appear in Europe in any way shape or form before 1.8 million years ago (that was Homo georgicus, which some think of as just an early Homo erectus or Homo ergaster.)In short, your teacher is dead wrong.

The graph you show is useful for figuring out brain size evolution, but unfortunately it is limited to fossils that included a skull. Basically it means we actually have more fossils than that graph shows.