I'm not sure which transmission you have, but I just finished overhauling mine on a Yanmar
3HM, a believe they all work basically the same way. There are 3 shafts, input (connected to the flywheel), output (connected to the shaft/ prop), and and idler (used for reverse).
The gears are always meshed and spin freely on the output shaft, both forward and reverse, obviously in opposite directions. The clutch
mechanism floats between the and engages one or the other. You should hear, and feel, a click when you put it into gear
-- it's spring loaded. It should also click onto neutral.
In your case, one side may be too tight -- do you have fluid? Since it's a friction clutch
with springs, there will always some some pressure, but they should slip freely. Of course, that doesn't mean the won't turn.
Have you tried turning the shaft in neutral with the engine off?