That's a rather simplistic definition of stoicism, don't you think?
You have to think about the context in which the Romans 'invented' stoicism. It is a notion of defending oneself from the tyranny of one's desires and fears. It is also a notion of isloating oneself from theeasy virtues described by the masses.
The main diffierence between stoicism and, say, puritanism, is that they say you should do it because it makes you stronger, and less foolish, rather than avoiding the wrath of God.
Personally, pursuit of pleasure can be just as dangerous as trying to avoid pain.
On the other hand, as I've said before, one has been given the capacity to experience pleasure and a fear of giving in to pleasure is no less stupid than giving in to pain.
Is that at all helpful? or even correct?