High winds do not hit your roof evenly across the surface. The corners, the edges of the roof, and the ridge line are especially susceptible to damage from high winds.
The wind can get under a corner or small piece of the shingle and curl it, or rip it off completely. This can leave your roof exposed in those areas, leading to leaks.
Another danger of high winds to your roof is “lifting.” While the shingles may look intact from the ground, high winds coming up over a roof can create a suction effect and “lift” the shingles upwards, loosening the nails which are holding them down.
When the shingles lift, the sealant between each layer can be broken, leading to leaks.
Additionally, high winds can blow debris around and cause trees and limbs to fall on your roof. Falling limbs can puncture the roof, or destroy your shingles, so be sure to cut down any trees which are overhanging your roof before any storms or high winds hit.
The debris that is blown around by the wind (branches, garbage, deck furniture, lawn decorations, etc.) can often be more damaging to your roof than the wind itself.
For more information, check out GAF’s article on how hail affects roofing shingles.