The blade adapter slips over the crankshaft before the blade goes on. The blade adapter is not pressed on or secured by a pin or set screw. There is a key in the engine shaft the blade adapter slides over to make it turn with the engine shaft. After time the blade adapter becomes rusted to the engine crankshaft and can be very difficult to remove.
You probably already have the lawnmower laying on the side. If not drain the fuel and oil and place the lawnmower on it's side. Spray the blade adapter liberally with Liquid Wrench, or some other rust buster. Tap down and up on the edges of the adapter with a hammer. The vibrations will help the rust buster penetrate between the blade adapter and the engine shaft. You might need to let the lawnmower set and reapply the rust buster and tap several times to break the adapter loose from the engine shaft. The blade adapter will eventually come free and you can remove it.
If you have a gear puller, remove the washers from the blade bolt, put the blade bolt into the hole it screws into and turn it at least 1 turn into the threads. Put the jaws of the gear puller above the blade adapter and screw the bolt in the gear puller against the head of the blade bolt. This will usually pull the blade adapter off the shaft.