On road conditions:
Main goal for motorcycles is maximum grip.
Main goal for cyclists is minimum friction.
More tire width = more grip = more friction.
This means that for a powerful motorcycle you need a wide tyre with more grip. But for a road going bicycle you have much less power and can have a narrower tyre for less friction.
In off-road conditions:
Main goal for both motorcycles and cycles is floatation over loose surfaces, maximum grip and resistance against punctures.
More width = more surface area = more weight without sinking into sand, mud and snow.
The weight of the vehicle demands a proportional tyre width to not sink into the terrain.
More width often comes with more sidewall. This dampens impacts and makes room for knobs that allow grip.
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