Why is a 2002 Honda foreman leaking gas out of the carburetor drain hole when drain screw is tight?

A couple of problems can cause this.

Turn the gas off and take the drain screw out. Look at the end, it should be a needle type valve. If the point is damaged or corroded, have it changed. Two dissimiliar metals combined with water collection in the bottom of the bowl causes this. It is good maintenence to drain the bowl every two or three tanks or at least quarterly.

Another, and the most common cause is the carb float is stuck in the up position. The carburetor needs to be cleaned if this is the case.