While the game doesn't provide this customized feature, you can make staffs, but they are like the existing ones. There is the special forge to do so.
I take it you're referring to the Atronach Forge at the College of Winterhold? If so, you've been rather badly misinformed: that forge only produces three conjuration staves, one for each atronach (flame, ice, and storm). It produces no other staves from the conjuration school, nor any staves from the destruction, illusion, restoration or alteration schools.
I've seen this rumor repeated in most every thread suggesting Beth add staff enchanting to the game; not sure why it won't die....