Some parents unknowingly sabotage their children's desire to take piano lessons. Here are some examples of what not to do, and what to do to correct it:
Put the piano in a "scary place" like the basement. Instead, put the piano in a more public place in the house where you can readily hear your child practicing and offer comments on how they're doing. The impact is three-fold: 1) If the piano is in a "public" part of your house, the child is more likely to walk by it and just start playing, even many times throughout the day, 2) it lets them hear positive comments from their parents about their playing and 3) it's not in a "scary" area to them.
Say "I don't like that piece." or "That piece sounds terrible!" Instead, help your child to "make friends" with pieces they may not like. If you say that, your child will be embarrassed to play it, won't practice it, and will end up staying on it for weeks because it will not be good enough to "pass" in the lesson.
Say "Stop practicing--I'm watching TV!" Instead, turn off the TV, listen to your child play the piano and offer them encouragement. Believe it or not, this happens more than you'd think. Students who are told this drop out of lessons sooner than students whose parents express positive encouragement to them while practicing.
Say "Do I have to go to the recital?" or "Don't sign up for that event." Instead, go to their piano events and sign them up for the "extra" ones. Think of how many baseball, basketball, etc. games you go to and how far you would travel for them. Would you stay in a hotel, or go out for ice cream afterward? Do the same for a piano event, such as a recital. If you complain about going and don't make it special, that tells a student that piano is not as important or as fun as the events you do endorse openly. The more events a student is involved in, the more motivated they will be to go further with piano lessons.