This is an excellent question, and one we feel like deserves a thoughtful answer! While we think all instruments are wonderful, piano is the one that stands out as a good choice for beginning students, and here are the reasons why:
First off, with a piano, the notes are already there in that once you push down the key, you get a sound. With a lot of other instruments, you have to create the sound using proper technique whether it be the bow pulling across the string with the correct dynamic pressure and finger placement, creating the proper intonation to play the pitch correctly, or whether its the correct mouth position needed to create a sounds when blowing through a wind or brass instrument. In many cases, it takes a certain level of technique to play a pitch correctly whereas on a piano, the pitch is already attached to the key, and voila! Just press the key, and there is the correct pitch!
Second, when learning how to play a piano, the student will learn the right and left hand parts equally, therefore they will be creating right-left brain connections that are so important for playing music and lots of other activities. Neither the right or left hand is more of a predominant participant in the process and this makes sure that both sides of the brain are being equally challenged by learning to play with both hands.
Third, learning how to play the piano is basically a way to be introduced to a very wide range of sound frequencies, as a student will be learning all the notes that fall within the high and mid ranges, as well as the lower ranges. The student will be learning how to read both the treble and the bass clef parts, which means they have more of a broad understanding of the whole range of pitches that are available to all other instruments!
Finally, because a student is learning the right and left hand parts equally, they can play the melody AND the harmony at the same time! With other instruments, usually they are only able to play one voice at at time which means that they usually need to play in an ensemble, orchestra or band to really enjoy the music playing process. With piano, the student basically has everything right in front of them they need to play!
Now, as a violin and guitar player myself, all instruments are amazing and good choices to learn how to play music with, however piano does have some unique characteristics based on the size and structure that make it ideal for starting one's musical journey playing.