Spindle won't shift? Hit it with a drift!
One side has a flange (Right?) the other side does not (Left?) Hit the side that does not have a flange with a drift punch and a hammer it will move, also you may want to open the pinch bolts a little with a big screw driver or a small pry bar, use some spray lube as well. Once it starts to move it will be a cinch.
Rusty
With Honda centre (sorry, center) stands (and probably other lesser makes too), all due to the lack of a bit of waterproof grease, the stand pivot tube usually ends up rusting nice and solidly into the stand itself (well, they certainly do here in the UK with the amount of salt they use on our roads in the winter!). The tube
should slide out reasonably easily, but rarely do.
Keep hitting the unflanged end of the tube too hard and you'll either seriously damage the part of the frame the stand is attached to, or, if it doesn't move at all, you'll burr over the end, and it won't then pass through the stand.
The tube's quite a close sliding fit in the stand, so capillary action draws water in all along the length, rust then starts, bonding the two together quite nicely.
Been there, cut stands off more than one bike..........
http://images.cmsnl.com/img/partslists/stand-cx500-1979-usa_bighu0112f5023_7c20.gif