The only reason why they where outraged when Spider became greeat Clan is because the Spider won and wasn´t defeated.
I can only truly speak for me, but I'm pretty sure it had a lot more to do with the fact that the Spider remained and continued to infiltrate the Empire, even after the Oracles/Iweko blatantly outed them as followers of Daigotsu/Fu Leng. The "Spider Project" should have been utterly finished as soon as the jig was up, but it wasn't finished. It continued to go on for many more years, and that simply strained credulity all the way to the breaking point for most people.