They don't hate them, despite Spider-Man implying they did.
The X-Men were in the right to be suspicious as Spider-Man had recently been Spock who had in the past tricked them and convinced them not to do a mind probe to see if he's who he says he is
Instead of agreeing to a short, quick, and painless mind probe (which Rachel only wanted to confirm he was telling the truth, not anything else) to ensure student safety Spider-Man guilt tripped them about Wolverine. That makes Spider-Man look like a jerk and very suspicious, yet the X-Men are portrayed as being in the wrong because it's Spider-Man. It is, quite frankly, poor writing.