What am I missing?
Mostly the fact that WE aren't moving at the speed of light, so we aren't really 12 billion light years from the point where the photons were first emitted. It didn't reach us until now because the universe is expanding, stretching the distances between the galaxies, which
really screws with the travel time of those stray little light beams. Toss in the fact that the cosmic expansion isn't constant, but is
accelerating, and the math to determine the travel time of our trans-universal photonic travelers gets REALLY fun. Have a
peek (and this is the simple version that leaves the acceleration math out).
Despite the fact that this light took 12 billion years to reach us, the originating galaxy was probably only 4 or 5 billion light years away when it was emitted.