Your ancestor may have not known exactly when he was born. I recently read through a Civil War pension application where the veteran was not certain of his year of birth. He made that same statement repeatedly throughout his pension paperwork. He knew that he was born in the very late 1830s, but that was ever as specific as he could get.
It is possible that your relative really did not know his precise date of birth, especially if he was born on the frontier and family effects were somehow lost or destroyed at some point in time.