Teachers don't matter

Proposition: Teaching staff (in aggregate) don't affect academic performance.

Proof by contradiction:
1. Assume teachers mattered and postulate two high schools, A and F.
2. Postulate school A is excellent with a California API of 930
3. Postulate school F is terrible with a California API of 530
4. Exchange all the teachers in school A with those in school F for four years.
5. If teachers mattered then the API of school F after 4 years should be 930 and that of school A should be 530.
6. Since 5. is clearly impossible, then the assumption is false and we have shown that teaching staff (in aggregate) don't matter.

Quod Erat Demonstratum (QED)

Not to say that an individual teacher can't make a difference, but honestly, not much.