The extensor muscles of the hip are indeed very powerful. However, the hip itself is a hinge joint; by definition, any movement from the hips is not necessarily going to be completely or even mostly vertical. Any movement that requires a big change in back angle, or a rapid hinge of the hips, will have both vertical and horizontal components as the back moves in a rotational pattern. That is, the shoulders start in front hips, then as the hips reach extension, the shoulders move towards the back of the hips. The bar or the lifter will move horizontally as a result of this, and in addition to following the movement of the shoulders, other factors will contribute to less vertical forces acting on the bar; the hips may extend so far forward that they bump the bar forward, and the lifter may shift his weight too far onto his toes resulting in his body moving forward after the second pull.
Taner Sagir is a good example of a (very strong, very talented) lifter with a lot of horizontal components to his pull:
1. The final joint that extends in his second pull is not the hips, but the knees (and ankles).
2. His hips extend to get his torso vertical and upright, but they never move beyond mid-foot, meaning he does not focus on throwing the hips forward or in front of him, but extending the legs as forcefully and completely as possible.
3. Because Apti's shoulders do not move far behind the bar, he does not have to struggle to get back underneath the bar or chase the bar forward as much.
Better cues that are used for the snatch and clean pull relate to getting the lifter to "get tall," which is itself a cue the focuses on vertical movement, or "push the legs," which shifts the emphasis of the movement from hip extension to knee or leg extension.
Move the bar UP. Use your legs.
Brent is the weightlifting coach at Dallas Strength and Conditioning. He has competed at USAW Nationals in 2015 and has been active in competition since 2006.