It says "Re'e Limadti Eschem Chukim u'Mishpatim" - just like I [Moshe, taught you] for free, also you [must teach] for free.

Suggestion: Perhaps this is so [even] for Mikra (written Torah) and Targum!

Rejection: "Chukim u'Mishpatim" - you must teach Chukim and Mishpatim for free, but you [need] not teach Mikra and Targum for free. (HA'AMUK DAVAR Vayikra 18:5 - Chukim are Drashos based on the Midos for expounding the Torah. Mishpatim are laws based on the Chukim.)

Question: We see that people who teach Mishnayos receive wages!

Answer #1 (R. Yudan bei R. Yishmael): They receive Sechar Betelah (compensation for wages that they could have earned if they were not teaching).

Answer #2 (R. Ze'ira): [They receive wages due to an enactment] mid'Rabanan. (They have power to enact unlike Torah law, for the sake of Torah.)