The last point is missing a crucial argument:If we would only hear these numbers they could both lie and it could be any even number. It is important that the second person says (correctly) "the person saying 47 is a liar", identifying that person as someone saying the truth.
The problem condition gets around that issue with the asserter of 50 calling the asserter of 47 a liar. If the number is not 50, then the asserter of 50 must be lying, implying that the number must be 47. But the number cannot be odd, thus the asserter of 50 must be a truth teller.