At an early age, very few children know what instrument they like to play, so often whatever instrument that the parent encourages the child to play is what he or she ends up playing. So the real question is what instrument should you choose for your child to play, and the answer is whatever instrument that you would like them to! Of course there are other constraints such as the cost of the instrument, the conditions at home in terms of tolerance of your neighbors to sound, and your own tolerance to "unpleasant" notes until your child starts playing half decently!
 
It may be said that the piano is inarguably the most popular instrument and the one most tried by children. The piano is certainly among the easier instruments to start playing, but it quickly gets complicated as one attempts to play with both hands and to play pieces other than the very simple ones. Because of the relatively easy start, initially there are fewer drop-out rates of children playing the piano, but on the other hand, when difficulty of pieces increases and they realize how much more practice and effort is needed to make progress, the curiosity and enthusiasm drops severely and children tend to quit. It is the role of the parents and the teacher to encourage them to practice and keep the interest high so that the child doesn’t give up.
 
The disadvantages of the piano are that it is bulky (in a small apartment, even a small upright may be taking up too much space), is loud (pressing the left pedal at all times while playing is not practical or pleasant) and in general is an expensive instrument (a decent sounding piano will cost several thousand dollars).