Eruvin, 73a: Indeed, based on the principle 'Kol ha'Moreh Halachah bi'Fenei Rabo, ¹ Moridin oso mi'Gedulaso', because Elazar issued rulings in the presence of Moshe, Yeshoshua never required the services of Elazar. ²

Oznayim la'Torah: Because he heard that after the war wih Midyan, Moshe would die, which he took to mean immediately - before he had the chance to teach Yisrael the Dinim - and this was borne out by the fact that Moshe forgot the Dinim. ¹ He also thought that, since Yehoshua was obligated to consult him, he must be Yehoshua's senior, which explains why he did not defer to him to relate the Dinim of Hag'alah. ²

Oznayim la'Torah: Because durng the war they had been permitted to eat the very same non-Kasher food that was absorbed in the Keilim that require Hechsher. He therefore needed to teach them that, although the Keilim in question did not require Tevilah during the course of the war, now they did, before they would be permitted to use them.

Oznayim la'Torah: Because he was contrasting the Din now to what it was when they went to war. ¹

Seforno: It refers to the Haza'ah with ashes of the Parah Adumah mentioned in the previous Pasuk.

Rashi: Elazar attributed the Halachos of Kashering Keilim to his Rebbi, Moshe (to stress that he did not hear it from Hashem but from Moshe).

Rashi: Because when he became angry, he erred and forgot them ¹ (and we learn from here that, woever gets angry, forgets his learning ? Pesachim, 66b).