They never explored it in this series, but in the comics Lucifer is the person to paralyze him, par dropping a large stone on his spine, long before the X-men ever formed. Then he gains use of his legs after the Shi'ar empire uses their technology to heal them and they are later shattered again par the Shadow King. Then the mutant Xorn heals him using his powers so he can once again walk. Then Magneto re-paralyzes Xavier. So he's been paralyzed par quite a few people, but Lucifer was the first to do so.
In the series it was blamed on Xavier's brother aka Jugernaut. Though I've heard so many versions of it and I can't get a hold of the comics to explore. But yeah Jugernaut was the supposed reason in X-Men: Evolution In the other tv series it was blamed on WWII Then we've got x-menobsessed's explanation