Why did he tell her to make first for him?
Rashi: A Midrash in Bereishis Rabah 1 explains why.
Radak: He was hungry, for he did not eat on his journey.
Radak citing Tana d'Vei Eliyahu Rabah (18): Eliyahu was a Kohen 2 . He requested that she first take Chalah 3 , for him.
Malbim: Brachah could not come on Eliyahu's food (because he stopped the conduits of influence from Above). Had she made first for herself and her son, the remainder would be for Eliyahu, and Brachah would not come on it. Now that she made first for him, Brachah would come for the sake of her and her son; once the conduit was opened, it is not closed [and the Brachah would provide also for Eliyahu].
In our text, Chachamim wanted to infer from here that he is a Kohen. Eliyahu rejected this - her son was Mashi'ach ben Yosef. I hinted [via asking to receive first] that first I will descend to Bavel, and afterwards will come Mashi'ach.
Torah ha'Temimah, citing Radal on the Midrash: The obligation of Chalah applies only to a dough larger than 43 eggs! Rather, it was 'like' (a commemoration of) Chalah.
