WHY IS IT DIFFICULT TO BREAK A SMALL WOODEN STICK THEN A LARGE ONE

PHYSICS,FORCE AND PRESSURE

The bending moment is greater when applying a force on a longer stick than applying the same force on a smaller stick.

If you were to imagine bending a long stick with both hands, then considering a free body diagram of the stick from its center to any of the forces, you will have to add bending moment, sheer and axial forces on the center piece that connects the rest of the stick. Using statics, since the object is in equilibrium, the net moment must equal zero: therefore, the bending moment + moment due to force applied by hand = 0. Bending moment = -moment due to bending force of hand

Since moment = F*d, greater distance means greater moments and greater chance of breaking sticks easily.

While breaking a large stick, you have a better grip, fulcrum, and leverage point. With a small stick, there is less surface area, so the idea is opposite.

By "small"you mean "short length" otherwise the question doesn't make sense.

It is torque that breaks a stick. On a short one, it take more force (hence it is more difficult) to achieve the torque necessary to break it.

Torque = Force*distance

hence, the shorter the distance the lesser the toque generated that breaks the stick.