From 35 years of experience teaching, (of which the first eight years we only taught one-handed backhands), the two handed backhand offers several extrensic advantages that both objectively and subjectively has proven more advantageous for almost all the 3000+ players I have taught:
1. It is easier for most players to first learn a two-handed backhand (and two-handed forehand too), and then, if they feel the propensity, switch later.
It is almost always far more difficult for players who first learned with one hand on the backhand to switch later to a two-handed backhand.
(There are some exceptions...I'm talking about the preponderence of general examples.)
2. I've NEVER had a two-hander not be able to hit a highly skilled one-handed backhand. I can't say for sure if it is just our methods of teaching, (or that we assimilate one-handed backhands for the slice very early on because we teach the correct volley skills very early on), or that the two-handed backhand as an initial learning method seems to help players understand the dynamics of a topspin backhand better and with a more repeatable, reliable swing pattern.
3. VERY few kids and even most adults, don't have the understanding, conception, or feel for hitting one-handed backhands correctly...even when they are given the proper dynamics to learn the stroke from.
Many players end up developing many flaws in trying to hit a one-handed backhand. They spend their lives then, trying to find quick fixes and bandaids to their most mediocre backhands. (A process many find a practice in futility!)
4. The most important aspect of any shot is the ability to create a reliable, repeatable swing path on command. This is where the two-handed backhand is superior as a stroke. Two hands, implementing both halves of the body, (and, as research shows, employs both halves of the brain better), players can create a far more stable swing that they can control and replicate faster and with more reliablity.
5. Two hands creates much better balance of stress, minimizing short and long term potential injuries.
The majority of players with tennis elbow are one-handed backhanders. It is almost rare indeed to find two-handed players get tennis elbow. (If they do, it usually can be traced to poor backhand volley form.)
These are just a few of the less obvious...but, in my opinion, far more influencial in terms of deciding to teach two-handed strokes.
Dave Smith: Author, Tennis Mastery/Coaching Mastery;
Senior Editor, TennisOne; Dunlop Master Professional