It didn't bug me as it's clearly for dramatic effect. Those corny things will always appear on tv/in movies to give emphasis to the importance of the answer...
To me it just felt like Angel probably answered Doyle right then and there but later on he was one his own, he repeated the statement to himself. Accepting the mission he was about to embark on but honestly reminding himself, or pepping himself up perhaps, that his was indeed game for it.