That's incorrect. Just changing a flywheel may not but a flywheel that has built in advance or advancing the timing will absolutely effect how an engine cranks over.
I guess I worded that badly.
Timing advance won't make the starter physically unable to turn the crankshaft a full revolution with the ignition off, which is what he described.
If the starter can no longer turn through the compression and you have not done anything to change the compression, (or intake/exhaust timing, etc) then your answer is most likely either electrical, (flat batteries, undersized wire, loose connection, bad ground, etc) or the compression release is stuck.
Did you have thr engine on its side for an extended period of time (like overnight) while doing the flywheel swap? Could be some oil in the cylinder, effectively increasing the compression...