"That's absolutely incorrect. You need flaps for both takeoff and landing. Lift and drag are proportional to the angle of the flaps, and as i mentioned before, higher flap "angle of attack" allows greater lift at lower airspeeds, allowing you to takeoff sooner."
No you are miss-understanding the point.
The most extreme flap angle is only used for landing, not for take off.
It´s there for landing, not taking off. Medium flap angle is for taking off.
You are absolutely right that it´s proportional, but you are completely disregarding that drag will overpower the lift because the drag will inhibit the plane to reach enough velocity to take off.
IT´s the same with F1 cars where eventually the downforce becomes so much that drag will disallow the car to hit it´s top speed it´s geared for.
Imagine a graph, vertical is lift, horizontal is speed.
The line can´t split itself so you need to choose what you want, with maximum flaps you go up the graph, with lowest you go horizontal.
Middle is a perfect ratio of taking off while maintaining enough speed to actually lift off the ground.