It's easy to roll your ankle on uneven ground if you don't pay attention to your foot placement. Especially on New England trail you have to constantly look to where to put your feet - usually planning 3 steps ahead to keep momentum going. Always remember to stop if you want to look around other then to glance up once in a while to see what is immediately ahead. Otherwise you'll fall down! 90% of what people see on an AT hike is their feet
Ankle strength has a lot to do with it, but mostly it's a matter of learning how to walk on rocks and making sure your feet land square, not at an angle. Every so often I'll zone out hiking an easy stretch then land my foot on something the wrong way and start to roll.
If you boot is too wide you can roll your foot inside the boot when walking on slopping rock, but that's a different issue then rolling ankles.