Alma’s declaration that he is a man should be seen as a parallel to King Benjamin’s similar declaration in Mosiah 2:10. In Benjamin’s case there was the implication that Benjamin’s status as king might elevate him to the status of god, and therefore he declares his humanity. For Alma, he has just wished that he were an angel, or a person from the realm of God, someone who was more than a man.
Alma quickly comes back to the essentiality of his humanity. He is a man, and not a being that is more than a man (recall the exchange between Lamoni and Ammon, Alma 18:17-18). This is yet another indication that the world of the spirit was not considered far away, and that there was popular though that beings from that world might be present on this earth. Of course Alma knows that the sons of Mosiah do not consider him more than a man, still he is careful to acknowledge his humanity as part of the process of separating the great experiences he has had from those things that he has done of himself. While a man, yet God worked through him. Alma is recognizing that distinction.