Why are valve clearances different on each valve?

Answer 1

Intake valves run cooler than exhaust valves and they are made of different material, so their thermal expansion is less than the exhaust valves. Therefore, they can have a smaller valve lash clearance, since they won't 'grow' as much due to thermal expansion, and won't present the problem of slamming into the top of the piston as readily as exhaust valves with too-small valve lash clearances will.

But, not all engines have dissimilar valve lash clearances on intake and exhaust. Many small single-cylinder engines have exactly the same clearance on both intake and exhaust valves.