The way it goes

I wanted to install a ceiling fan where there was only a ceiling light.  No problem!  I've done this many times before - maybe 30-45 minutes is plenty.

HAHAHAHAHHAHAHAHAHHAA!

As so often happens in projects, this one snowballed and wound up taking over 3 hours.  Follow along with these easy-to-repeat steps and see if you can tell where the problem lies:

Step 1 - Remove the old light fixture

1. finger screws for the glass bowl -- easy peasy.
2. a screw or two holding the light housing to the junction box -- boy, this box is pretty wiggly.
3. the wirenuts and ground wire connecting the light to the supply -- hot wire is off; all is well.

Pro tip: It's a good idea to turn off the breaker, but chances are good your breakers are labeled incomprehensibly or are outright lies.  What I do is turn off the room switch and then quickly tap the hot wire with a finger to see if i get zapped.  I didn't this time!

Surprise! A pleasant surprise!  The power supply run to the light is actually 4 wire romex ("12-3"), which is convenient for fans (one hot for light, one hot for fan, one neutral, one ground).  There was only one switch in a one-gang box, but hey - somebody was thinking ahead.

Surprise! An unpleasant surprise!  While fiddling with the wiggly box, I got zapped by the white wire.  That's bad - the white wire shouldn't be hot... not with the switch off, not with the black and red being unpowered.  Investigation required.

In any case, to hang a fan I'll need to reinforce the box - I can inspect the wiring when i get up in the attic.  The box was using one of those metal hangers that span between the two joists, but it seemed to be quite loose.

Step 2 - Reinforce the ceiling box

Up in attic (getting to the area above the box was a challenge to begin with!) I found that the hanger hardware was poorly installed.  Each side had metal brackets with three holes for nails, but each side was only held on with loose staples.  I pulled them out and put in screws (easier than nails in this case).  That cut down a lot of the wiggling, but it still twisted more than i'd prefer, and i didn't want the fan rocking, so...

I cut a 2x4 to the width of the cavity and screwed it in - some of the angles were pretty hard to get to, but i did it... slightly crookedly.  So i reattached the junction box with some shims to make up the difference.  Perfect!

Step 3 - Run new wires between the ceiling box and the wall switch

Luckily i had an extra length of romex laying around.

Step 4 - Replace the wall switch with a 2-gang box and wire new switches

Luckily I had some extra old work junction boxes and switches laying around.  I'm not sure what was causing the white wire to be hot, but when i was done all was well.  Something must have been shorted in the switch box before i pulled it all out and rewired.

Step 5 - Install Ceiling Fan

Connect the new wires, attach the new base to the ceiling box, connect the blades.  Test (all went fine).

Conclusion

Aspiring do-it-yourselfers beware: this is a disturbingly common occurrence.  Not always ceiling fans, but houses are generally built by drug-crazed vandals.

To answer the question at the beginning: "see if you can tell where the problem lies" the problem was the existence of steps 2,3, and 4.  Ideally you'd only need 1 and 5 (but only 1 of the 3 ceiling fans i did in this batch was actually like that).