I'm sure that in every field of human endeavor there are misconceptions, old-wives-tales, and out-and-out untruths that go unquestioned, are handed down through the ages, and which ultimately lead to all sorts of problems if believed and adhered to without question. Piano is no exception.
Throughout my early years of playing and studying the piano, my teachers, and many others, imparted many ideas and methods which, being young and naive, I of course accepted as fact and as being the only way to play. I later learned how many of them were simply wrong. Here are some of my "favorite" misconceptions about playing the piano:
1. We play with our fingers. Of course the fingers are the point of contact with key, but to say they do all the work would be no more correct than it would be to say you dance with your feet. The movements of the hands, arms, torso, and legs (for support and balance as well as pedaling) are all coordinated and the fingers transfer the power or energy to the keys. I strongly discourage any aspiring pianist to do exercises that promote "independence" of the fingers. A technique based mostly on finger movements or training the fingers separately will produce mechanical-sounding playing, and in most people it will cause strain, pain and potentially injury over many years of playing that way. It's also untrue that you need "fingers of steel" or a lot of strength in the fingers. If you watch little child prodigies of age 5 or 6 play, you will realize they have very little muscle strength. Instead they have flexibility, coordination and speed, which enables them to play most of the difficult pieces adults play without having had years of building up muscle strength.
2. To get a rich or "singing" sound, you must depress the key all the way to the keybed. A very famous pianist who was my teacher for a while told me this over and over. However, the physics just don't support this theory. There is a point at which the hammer is tripped, and pressing the key past this point is pure wasted energy. You can feel that point on any given piano by pressing the key slowly, and where you feel the resistance is where the hammer will be tripped. It is a highly advanced skill to have laser-like focus and deliver your power precisely to that point and not past it, but it is a skill worth developing. You don't get loud or powerful playing by aiming deep either; you get loud playing by having greater velocity (speed) of the hammer hitting the string. To get a rich and singing tone, as many call it, is a function of many aspects of playing coming together, such as phrasing (which I might describe as blending small movements into larger ones to create a long line), nuances in timing and dynamics, having the fingers, hands and arm be supple and relaxed to transfer power to the keys, and emotional involvement which brings it all together.
3. Playing by ear is "cheating." So many people come to me and, when they are reading a piece of music will say, "I'm not really reading, I just know this song so I'm pretty much playing it by ear." To which I say, bravo! Being able to play by ear is the ultimate show of how well-developed your ear is. It's funny, isn't it, that we idolize Mozart because he was able to hear a piece once and play it by ear, but if the rest of us do that (at least in part), it is considered cheating, and not the "real" way to learn. This is so preposterous.
I often have students learn entire pieces by ear (I play a phrase for them --they have eyes closed -- and they play it back). This is wonderful ear-training (and it simultaneously trains the memory). It is a joy to be able to just sit down and play by ear. For the pieces we simply can't learn this way, or we could but it would be too time-consuming, we have the written page. For that reason it is highly desirable to be a cracker-jack sight-reader as well, which I also teach. But playing by ear and using the ear to the greatest extent possible is to be encouraged, not disparaged.
4.To learn a piece, you should start by playing it slowly, hands separately. I believe there are far better ways to begin a new piece. Hands separately does not enable you to hear the whole texture, the complete harmonies. Educating the ear is perhaps the most important aspect of learning music, so if you are not working towards that, you are not being efficient and effective in your practice. Hands separately is just not the same coordination as hands together; it is a huge waste to spend so much practice time with one hand in your lap. Slow practice has its usefulness, but it also encourages inefficiency in technique and you may find, for example, that you use a fingering which works fine for slow playing but not necessarily for fast playing. I teach a method of learning called outlining, where you play a "sketch" of the piece. You play the essential structure of the piece, adding more and more details each time in an improvisatory way, and always hands together. You try to play it at the actual tempo of the piece, or as close to it as possible. When you become skilled at this method you can learn a great deal of the piece. Later on, you will probably need some slower practice to work on technical details that can not be mastered simply through outlining. But at least now you confine your slow practice to those passages which really require it. Going through an entire piece slowly with hands separately can be a huge time-waster. See my post on outlining for more information on this fantastic technique.
In summary, you shouldn't always believe what you were told about playing the piano (or anything else for that matter). If you feel that your practice time is not getting you the results you want, or that your playing lacks the speed, power, delicacy, subtlety, or any other aspect that you desire, question every assumption you have made. You may be operating under some major misconceptions.