What is pedantic speech?

Not a medical term. Pedantic speech is speech intended to impress people with how smart the speaker is. An example might be using the term cephalgia when the more common word headache would do just as well. The term is also applied when a speaker is overly concerned with exactness. The term is frequently used as a criticism to imply that a speaker has trouble relating to the listeners.
Asperger soeech. Pedantic speech is overly formal or complex speech. People with Asperger syndrome often have pedantic speech that sounds odd to others. They may not use slang or understand that most people use different ways to speak to teachers and peers.