More than a few times, I've introduced someone who doesn't regularly game to a game and that person chooses to skip the tutorial. Sometimes, they skip the tutorial right away. More often, they start the tutorial, then become impatient and skip to real gameplay.
It mainly has to do with pace. A tutorial shouldn't be too much slower than normal play. It must be fun in its own right.
In some games, it can be better to start the player off with the full palette of actions among easier enemies and challenges. Allow the player to learn through experimentation, rather than overt instruction. That's not feasible in all games.
In any case, all tutorials should be true play -- not a precursor to fun, but actual fun.