Welcome to what will hopefully be a rewarding and lifelong addiction!
My own understanding of the reasoning behind pivoting/performing a Tenkan movement on the balls of your feet instead of the heel is that this is the only way to consistently keep your weight predominantly forward and thus maintain proper balance and extension throughout the turn. (You'll find as you progress that a great deal of your Aikido practice will deal with exercising a means of being able to maintain your balance and rootedness even while moving or starting and stopping movement quickly.)
So this only makes sense when you place this particular movement in the context of an actual Aikido technique, which of course would be performed in response to an attack (the Tenkan is not an end in and of itself, but often forms the opening or middle of a technique leading up to another kind of movement used to subdue an attacker). If one tries to perform the pivot on their heel, they are forced (just by virtue of one's body positioning) to let their body weight rest back towards their rear (which can ultimately put you in a precarious position should your attacker try to push or pull you off balance while you are performing a Tenkan); keeping your weight primarily forward throughout the turn not only keeps you in this more balanced state but also lets you maintatin martial readiness/the ability to react quickly (ie. turn to face your attacker) in the event that he or she tries to resist your technique. There is at the very least a half-second or so of time that is lost if you have to shift your weight forward in order to react, and though it seems like just a short period of time to regain your balance and momentum, this may make the difference between you being able to react quickly enough to strike back or avoid getting pulled off balance or struck yourself.
Hope this helps!