Why does watching which slit a particle goes through destroy the interference pattern?

Checking the route writes a record, and the stripes form only where no record of the route exists. While nothing records which path a particle took, the amplitudes for the two paths add and cancel. A which-path detector ties each path to its own detector state. Make those states perfectly distinguishable and the stripes vanish. Make them partly distinguishable and the stripes partly fade, and for evenly split paths the contrast left equals the overlap of the two detector states. Repair itself is such a detector. Put an empty seam, the boundary two neighbors share, and a seam holding one unit into superposition, then let one repair act. Recording how many units crossed leaves most of the pattern. Writing the seam's parity as well, whether its count is even or odd, makes the bands go flat at three eighths.

Also in Chapter 19: Why Can't You Ask Everything At Once?, Chapter 3: Why Would a Universe Need Anybody In It?.