Remove the spark plug wire, turn the mower on its side with the gas tank upward, put a socket or wrench on the bolt, hold onto the blade with a gloved hand and use a pipe on the end of the ratchet or wrench, if necessary. It will come out.

Tip the mower up on it's RH side wheels (carburetor up). Remove the bag or mulch plug - this cuts off the ignition. Remove the spark plug wire anyway. Rotate the blade until it's straight up and down, and place a piece of 2x4 wood in the deck on the RH side of the blade. Stand on the wood and put the 5/8"* wrench (may have to use a breaker bar or at least a 1/2" drive ratchet) on the bolt head and put your weight on it to turn it COUNTERCLOCKWISE, or LEFT. Do the opposite to install the new blade.
*some have a 9/16" bolt

If you have already tipped up the mower on the wrong side, you will have to replace the air filter if oil-soaked, and you may have to take the spark plug out and pull the starter cord (be sure to GROUND the spark plug wire on the post provided to the left of the spark plug hole before pulling the starter) about twenty times to blow the oil out of the cylinder. Put the plug back in, connect the wire and check the oil. If all good, start the engine. It will blow smoke for several minutes. Don't do this again, unless you like the remedy.

Coincidentally, I just got through changing the blades on my 10684 and 22271, which are exactly alike as far as the blade and driver.

Thanks for the tips above. I was having same trouble with my Lawn Boy 10247. What worked was:

1. Get 4 equal 5 gal buckets and put the mower up on them.
2. Spritz with ~WD-40 and wait an hour or two, have beer and supper.
3. Use a 15/16" socket, 1/2" drive.
4. Righty-tighty, lefty-loosey.
5. Whack the socket wrench with a rubber mallet about 3 times to loosen.
6. Sharpen with diamond blade on 4" grinder.
7. Check balance, reassemble, mow.