Two strands of extremism

I can understand some Brits being converted to Muslim sympathizers because British troops have been involved in the Middle East area for over a century. One might expect some retaliation as has occurred by extremists of one strand, the pro Muslim.

And that retaliation would incite hatred of  Muslims by extremists of the other strand, the anti-Muslim. .

Pulling troops out of Muslim areas should help quell both extremists. What in the world are the troops there for?