At speed, a cyclist pushes the right handlebar to start a right turn. Why?

Answer: It creates the right lean

It points the wheel right — Common guess, but backwards for the first instant. Pushing the right bar steers the front wheel left, so the bike's support path moves left and the bike leans right. Only after the right lean is established does the wheel steer into the right turn. This is why countersteering feels like a trick until you notice that the goal is lean, not simply pointing the tire.

It creates the right lean ✓ — Correct. A bike must lean into a turn, and countersteering is the quick way to create that lean. The Berkeley AJP paper states the counterintuitive rule directly: to turn right, steer left initially. Jan Heine describes the same sequence in riding language: steer outside the curve first, then the bike leans into the turn you actually want.

It moves body weight — Close to what riders feel, but not the mechanism in the sources. The cited countersteering explanations focus on the handlebar input first steering the bike the wrong way briefly, which creates the lean. Body position can matter in riding, but this specific push works because it changes steering and roll, not because it simply shifts weight.