AP or AD Teemo?

If by AD you mean on-hit with bork and mallet, then it is good for split pushing and dealing with tanky opponents. Also note that you are then harder to counterbuild as you deal mixed damage. But if you want to actively help your team better pick AP for shrooms and blinds. With on-hit Teemo, it is hard to deal damage in teamfights without dying quickly; this applies for AP too, but at least you can blind-AA then run.

Personally my teemo build depends on my lane opponent; different builds have completely different impacts on how the matchup ends.

AP. Never look back.

Is there any reason not to go AP?

AP would be better. Kinda bad for going AD because:

Q- A simple blind with no damage. W- Unaffected E- Auto-attacks boosted with very minimal damage R- Just an AoE slow with no damage.

They have different capabilities.

Go AP if you want to annoy your enemies with stupid damage on Noxious Trap and Blinding Dart, but have very little staying power in a fight. Go AD if you want to use your status effects for utility, your primary damage will come from your autos while you got great chasing with Move Quickly, and the addition of magic damage with each auto through Toxic Shot will make it harder to itemize against.

ALWAYS AP