Let's look at Yamaha's MotoGP challenger, the YZR-M1. Figure 1 (above) is a side view showing the basic layout. Long, long swingarm, rear engine mounts just above and below the swingarm pivot and long thin "hangers" descending from the frame to connect the front engine mount. Figure 2 (left) is a top view. We will hold the front part of the frame (steering head area) steady and put a side load to the left against the end of the swingarm. What happens? The swingarm is a pretty long lever, connected to the engine quite rigidly (in terms of lateral forces) because the rear engine mounts are close to the pivot. The swingarm tries to move the engine. If the frame on each side can twist in the area above the swingarm pivot (and the M1 frame is quite thin here), a pivot is created approximately where I've drawn the quartered circle. The rear of the swingarm goes to the left, while the front of the engine tries to go to the right. The front engine hangers, being thin and long, can provide little resistance, and bend to the right. The overall result is the rear wheel, as shown by the dotted lines, moves to the left, steering to the right.