Because that is what is usually asked for! But seriously, a principal looks at things from a managerial perspective, where as a teacher's perspective is that of day to day operations. So if a teacher speaks highly of you, that will not carry as much weight in the decision-making process as the same words spoken by a principal. If the teachers are your peers, they might let the fact that they like you and get along well with you color their assessment of your job performance. The principal is one step removed from all of that, and is considered to be more objective in his/her assessment of your skills for the position to which you are applying. Make sense?
To "piggy-back" on Kim's answer, getting referral from someone in a managerial position normally holds quite a bit more weight than referrals from peers/friends/former teachers, etc. In my experience in the military and now business world, this holds true.
The way that it was explained to me is to think of a manager as a plane flying at a high-level (30ft-40k ft) while those who work for them may be a little more into the details (maybe at 10k-20k ft altitude) not seeing from the same lense as their manager; in this case lenses could be whatever subject that the teacher is specialized in. As Kim said, it allows them to see your performance/potential and contributions to the organization, "one step removed" from where you currently are.
I hope that this helps and wish you nothing but success!