User blog comment:B214/Volume 22 spoilers/@comment-95.90.227.74-20161018202609/@comment-29963364-20161018210201

There's still the matter of his soul.

Issei's new body is made from Great Red's flesh, and Ophis used her power to permanently bind his soul to his new body. So you could say that the two most powerful dragons in existance are his second parents (in a way). But since it's still his original soul, Mr & Mrs. Hyoudou are still his parents.