I see what you mean...
Hang on, brain melting...
OK, gotten to the bottom of it....
Nicked from elsewhere on t'internet
The issue is that the question has been specifically worded to cause to differing opinions in two types of people.
The practical thinkers will assume that the plane is using it’s engines and that the thrust will simply push it forwards, regardless of the conveyor’s speed, as the frictional force between the conveyor and the wheels is negligible and the thrust from the engines acts upon the air and not the wheels. They will say the the plane does take off, and they’d be correct.
However, the theoretical thinkers will ignore the real-world practicalities of the situation because it would never exist. Instead they abstract it to a simple object with a given speed, which is being kept motionless by something exerting a force in the opposite direction. They correctly calculate that the net speed of the object will be nothing and therefore there would be no airflow over the wings of the plane to allow it to take off.
i.e. If the plane applies no power and the belt moves -10 ft in one second, then the plane moves 0 + (-10) = -10 ft. However, if the plane applies power to move over the belt at +10 ft in one second, then you have +10 + (-10) = 0.
This assumes you are matching wheelspeed to belt speed which is one of two possible interpretations, the other that you match belt speed to ground speed which results in wheelspeed double the groundspeed.
In reality, both answers are equally valid depending on your point of view and how you interpret the question, which has been worded very badly (on purpose, I’m sure).
Which explains why this is a conudrum which having no looked is all over t'internet and not a straight forward question and answer.