From the NOAA:
It is our contention that highway overpasses are inadequate tornado sheltering locations for the following meteorological reasons. First, ALL tornadoes have some amount of debris within their near-surface flow. In the case of a strong or violent tornado, much more debris would be present, traveling at much higher speeds, especially when debris from man-made structures is involved. In strong and violent tornadoes, typically harmless everyday items such as shingles, boards, pop cans, dishes (or pieces thereof) become dangerous missiles and are responsible for most tornado casualties. Second, by climbing up under an overpass, people will be exposed to higher wind speeds and more flying debris. Third, the narrow passage underneath an overpass might cause an increase in the wind speed under the bridge. The extent to which this is true, and the circumstances under which it could happen are not known, but this is at least a possibility. Fourth, most overpasses don't have girders or support beams for handholds or small ledges into which to crawl. And, finally, if an overpass is directly in the path of a tornado, the wind will change direction nearly 180 degrees as the vortex passes. Thus, if one side of the overpass was protected from the highest wind speeds as the tornado approached, that same side of the bridge will be completely exposed to the wind and flying debris as the tornado moves away and vice-versa.
Seeking shelter under a highway overpass is to become a stationary target for flying debris, with a substantial risk of being blown out and carried by the tornado winds. Safety in such a location is merely an illusion. Further explanation of all of these points, with examples will be given in the slides to follow.