At first i assumed the professor meant that, so all the classics like eduMAcation and absoFREAKINGlutely and others came to mind, but he said "The one". Since those are all so common in slang i feel safe to assume there is either "One" word or a trick question of sorts.
This text makes an interesting point: run->ran or man->men are infixes: http://www.csun.edu/english/english302/morph.pdf
If adding -ed is a suffix, then internal changes to denote tense or plurality are, logically, infixes. However, this doesn't answer your professor's question as it suggests that a small group of words have infixes, when showing tense or number.