NOW Say I get along side the treadmill, and push the plane. It wont matter how fast the treadmill goes in the opposite direction, I will still be able to push the plane. The engines are the exact same thing.

However much forward force you apply with [your hand] or engines, the exact same amount of force will be applied in the opposite direction by the conveyor belt on the tires. That force will act to accelerate the spin of the wheels. And forget about bearing friction (and wheel/surface friction too). Things like that don't belong in thought problems like this. The force the conveyor belt applies to the wheels is not acting against friction. It is acting against the inertia of the wheels. It accelerates their spin. This is the factor that is ignored by the people who say that the the wheels "decouple the plane from the runway".

You might ask: "what if I put the plane on the conveyor belt, and then [push] it along at 10 meters per second with [my hand]?" Well, that is a logical impossiblity. You cannot have the wheel speed match the conveyor speed, no wheel slippage, and still move at 10 meters per second. It is like asking what happens if you're tied to an immovable wall with an unbreakable rope, and you start to walk away from the wall at 10 m/s. You can't even start to answer, because the question itself is impossible. All the conditions of the question cannot possibly hold true. In the airplane question, this problem arises if you specify that the wheels are massless, because it doesn't take any force to spin a massless wheel, and so the conveyor belt cannot apply a backward force to the plane. In this case, the question is logically inconsistent.