"I checked the lacing and it looks right! What the heck did I do
wrong??"
I forgot, did you say you were using the old rim or a new one? If the
old rim were badly bent, it could do this.
Another possibility might be that the spokes you're using are too
short, so by the time you get the first half of them laced the second
half of them won't reach the nipple. This could happen if you changed
the hub or rim from what it was before and the bike shop that sold you
the spokes calculated the length wrong. But like the other posters
said, it's really hard to say without seeing the wheel.
You're keeping the first spokes you laced really loose, right? Just
engage a thread or two to start. If you still have this problem and
you're sure it's laced right, I think it's got to be either a bent rim
(if you're using the old one) or the spokes are too short. Being only
a mm or two too short will mess you up by the time you lace the last
spokes. The length difference adds up.
Back in the days of antique cars, when they made each automobile wheel
with 10 or 12 wood spokes inserted into a steel felloe, they auto
manufacturers had to either set up a special machine shop to cut the
wood spokes to exact length, or buy their wheels from a specialty
wheelmaker like Kelsey-Hayes. If they tried to cut the spokes in the
automaker's wood shop, where tolerances were customarily held to +/-
1/64", the spokes would fit too tight or too loose because the
difference adds up each time you insert a spoke. They had to hold the
tolerance to +/- 1/128". Even then, during the summer when the wood
spokes would dry out and contract about 1/256" in length, the wheels
would start to creak a little due to loose spokes.
I restored a 1922 Dodge Bros. touring car a few years ago. Did you
ever try to find a shop that will cut a wood spoke to +/- 1/128"? Not
too easy to find.