Your question is interesting, as Jesus as identified Himself with other virtues and concepts (“I am the Truth, the Way and the Life” “I am the Light of the World” and “God is Love”).
However, he never identified Himself as literally Faith, but considered it as a very important virtue for us. I think it has to do with Faith being a temporal Theological Virtue, as the only Theological Virtue that stays after death and resurrection is Love; so he cannot be (eternally) Faith. Nevertheless, Faith is a critical tool for calling us in this temporal life.