I'm working on template routing some pieces for a project right now. Had a consultation with @thewoodwhisperer because I was having trouble with the template routing and needed some other project advice.
i had similar problems with parts catching the bit and wanting to tear out of my hands... It came down to the direction I was routing. I was going against the grain and onto end grain and it was catching on that. I've since been paying more attention to grain direction, even switching the side of the piece that the template is on to make sure I'm not taking the router bit against the grain and it's been a lot better. Like hand planing, you want to go in the right direction with the grain
having a spiral cut bit helps, too.