In My Darling Clementine Doc Holiday doesn't seem like he'd have any sensible reason to want to fight Wyatt. Why does he want to challenge him to a gun fight?
A simple plot device. Clementine Carter is not a historical person, and in this script appears to be an amalgam of Big Nose Kate and Josephine Earp, according to Wikipedia.
In the film, Clementine was known as previously being involved with Doc Holiday. Thus Wyatt Earp's interest in her caused conflict.