It is necessary when asking a question like "Whom do you love (between me and X)? = Tu pe cine iubești (dintre mine și X)?" which assumes that the object of love is part of a larger set of lovable beings and the lover states his or her choice. The answer can be either "Pe tine." or one of "Pe tine te iubesc. / Te iubesc pe tine." In this circumstance, answering "Te iubesc." doesn't work, because the question asks for WHOM, not for WHAT.

If the question would be "Mă iubești?" then the answer would be "Te iubesc.", without "pe tine".

It's not necessary in normal circumstances, so it's most likely just a mistake in the course.