The one-handed backhand is a less common but in many ways more effective shot in todays game than a two-handed backhand. The reason many pros don't use it is because they are reluctant to change due to tournament pressure at an early age. Some of the best players in the world, including Roger Federer and Pete Sampras dominated the courts with their one-handed backhands. In fact, Sampras switch just before turning pro as a teenager because he was convinced it would help his game. The benefits of the one-handed backhand over two-handed backhands is a wider court coverage with better reach, and usually better hand-eye coordination for other backhand shots like volleys, slices and drop shots. The drawback is that high balls are more difficult to return with a one-handed backhand. I recommend giving each backhand a fair chance to learn and experiment with before choosing the backhand that you feel most comfortable with. You may even have a change of heart over time. But it is generally taught to adults learning how to play tennis.
Grip: Eastern and Semi-Western Backhand Grips
How to Hit a One-Handed Backhand
*Try to have patience with the sound quality of this video, because this coach is excellent.