ok, if you think the timing looks right (the magnet location) and you are getting spark, pull the carb apart and check the main jet.
what gearnut said is true, a spark plug will spark much easier when it's layng on the head. add in compression and all that and it's harder for the plug to make a hot enough spark to fire the fuel.
do you have anything hooked to the white wire? (a headlight perhaps). if so, get rid of it and cut the white whire off. any time you connect something to the white wire, it pulls power away from the cdi. you can still get spark, but it won't be enough to fire the engine.
get rid of the stock spark plug wire and put an automotive wire on it with a rubber boot, and go to an ngk plug.
seriously, if it has spark at the right time, it should have fired on starting fluid.
you may have a bad plug, a bad wire, a bad cdi, a weak magneto, a wire grounding out somewhere...it can be a number of things at this point.
I would pull the carb apart, check the main jet and make sure nothing is blocked. then, i'd swap out the plug and wire and check the wiring.
this thing should run if you have fuel, spark at the right time, compression and air.