In the first X-Men, we're told Magneto helped Charles build Cerebro. In The Last Stand, they take that a step further, and show him as being another teacher or administrator at the school. These prequel film seem to leave no room for that.
shareThe Cerebro that was at the FBI facility in First Class was destroyed when Shaw raided the place. Xavier had to build his own in the basement of the mansion and Mangeto probably helped him do that before their falling out.
The beginning of X3 where they are meeting a young Jean Grey together did not indicate that they worked together at Xavier's school. It just meant they came together to approach the potentially most powerful mutant they had ever encountered. They came together several times over the years for various reasons. It doesn't mean they were on the same side or that Magneto was another teacher at the school.
actually it was heavily implied that they were recruiting new students together for the school.
"we wouldn't need to meet everyone of them in person" said Eric.
there is no contradiction, it simply means they became friends again at sometime before this.
he probably built the Cerebro bellow the mansion during "first class" during their time training at the Mansion but we just didn't see it in the movie.
my guess is that in the 80's Charles started becoming immune to the serum that allowed him to walk and his powers started to gradually come back. he started using Cerebro again and read Eric's mind and realized he was trying to save Kennedy and didn't kill him. Charles forgave Eric and probably let him lose, and they became friends again and Eric joined his school.
then Eric found out about Mystique being held captive and experimented on and went off to rescue her.
he found her in a terrible shape inside a tiny cell unable to move, with scars on her head indicating some of her brain tissue was removed, barely able to speak and not even remembering parts of her past (which is why she didn't even remember her son Nightcrawler later)
when he saw what they did to her and other mutants he became enraged again and wanted to take action to ensure mutant security. Charles disagreed with his methods and so Eric left to form his own brotherhood instead.
after a while Charles's spine began to deteriorate again because the serum stopped working. but he could still walk when he rescued Scott and other children from Striker's island lab. after that he had to start using his wheelchair again permanently.
the same later happened with Hank when he became immune to the serum and got stuck in his animal form.
I didn't realize Hank had become immune I always assumed he'd just finally come to terms with who and what he was
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