There are thousands of undersea earthquakes every year, some of them quite powerful. Why do they so rarely cause tsunamis?
Tsunamis usually happen along subduction zones, places where one crustal plate is moving under another. One side of the fault has to move upwards significantly to produce the wave. Most undersea faults are transform or strike-slip faults, where the two sides move left and right, not up and down, so no wave is formed.