Why is sound not classified as an electromagnetic wave?
Sound is a mechanical wave.
Electromagnetic wave is a by-product of both electric and magnetic field. It does not require presence of any medium and can travel through vacuum.
Whereas mechanical waves requires the presence of medium. It works by pushing medium's molecules and traveling through it. Sound works this way. Sound also is not the by-product of electric and magnetic field, it is rather the vibration in the medium.
What we perceive as sound is the vibration that comes to our ear and our brain analyses it.
The perfect example to notice this is on a speaker's diaphragm. When you will increase the volume, you can see or feel the vibration more vigorously. You can also check this by keeping your hand on your throat and then hum or talk to feel the vibration.
What vibration does that it pushes medium's molecules and you can't push anything when there is no medium and that's also why density of medium lower the volume of sound.
That's why Sound is a mechanical wave and not an Electromagnetic wave.