What kind of puller are you using? The right one is a crowfoot-shaped one that uses the two threaded holes in the center of the balancer, and the puller screw bears against the end of the crankshaft. If you use a jaw-type puller on the outside, you'll tear the outer ring off, or damage it to the point it will separate when the engine is run again. If you're using a heavy-duty harmonic balancer puller, tighten it very firmly, then smack the end of the puller center bolt with a BIG hammer. Once the shock breaks the balancer loose, it should come off pretty easily. It's probably on too tight for penetrating oil to do much good.
As a last resort, use a rosebud torch to heat the center hub of the balancer while the puller is tightened down. That usually ruins the balancer, but it will get it moving so you can do the rest of the engine teardown.
Jerry
