It's not really required. The "rule" is that you put first whichever object is shorter, because in that case the preposition + pronoun become an enclitic and lose the stress. In this case, that is אותך.
Both can follow להציג. However אותך means that "you" is being introduced and לך means that someone or someone else is being introduced "to you". Here, only אותך works, because "you" ia being introduced "to the parents".