What was the exact reason Frank was banished from Tomorrowland?
We are never told:
We’re never explicitly told, but it likely has something to do with Frank’s tachyon machine, called the Monitor. After predicting with 100% certainty that the people on Earth would destroy themselves, it seems that Governor Nix (the leader of Plus Ultra at the time) took a hardline approach to +U isolating themselves.
The film only tells us that he was exiled after completing work on the Monitor. The feeling I got was that Nix’s isolationist policies caused a lot of friction in the ranks of the organization, leading to the banishment of people like Frank. Source
Some details at the wiki:
Nix appears to greet them, and takes them to a building linked to a tachyon machine designed by Frank that can show images from the past and future, from which Casey learns that a worldwide catastrophe will happen in the near future. Because of this discovery, Frank lost all hope and was banished from Tomorrowland.