The clutches have to have a way to drive the shaft, so there is either a spline or a square running through the clutch parts. The square is cheaper, the spline is better; since 1930s Bugattis, cars have just about always used splines (some old Bugattis used a square shaft through the clutch, and it was a lousy idea). It is common in high torque situations that the shaft wears a bit so that eventually the clutch parts will not easily slide sideways: a step forms at the boundary of the normal running position. Also, there may be some fretting corrosion, which packs the clearance and makes the clutch parts a tight fit on the shaft, despite their wear. However in your case, I do not see how anything can come apart until you unscrew whatever is being held by the thread you showed in your photo. You haven't shown us the other side of the clutches, so we can see if there is a thread there too. Meanwhile, I think it would be a terrible idea to use force to separate parts that are probably being held in position by a screwed-on locking collar.
