A child ties a rock to a rope and turns it around describing a circle. horizontal. My Classical Physics teacher has told me that the string cannot be perfectly horizontal, but I don't know why. I have tried to make a balance of forces, but I don't draw any conclusions.
There is gravitational force pull the rock down, therefore to main rock's position in height, the string had an angle with respect to horizon and therefore produced an upwards counter action force.
Draw a force diagram at any one instant: There are only 2 forces acting on the rock, gravity which points down vertically, and the tension force from the string. Look at the vertical direction. We want the rock to be making horizontal circles so it can't be moving in the vertical direction. This means the forces in the vertical direction must be balanced. If the string is perfectly horizontal there can't be a force to balance the force of gravity in the vertical direction because there are no other forces at play (neglecting the air). The string tension must have at least a vertical component that cancels out the force of gravity. No matter how strong the string tension is, there's no way for a purely horizontal force to cancel out a purely vertical one.
Your teacher is correct about it, since the ball is in vertical equilibrium and hence forces are balanced in the vertical direction meaning that a component of tension balances the weight of the rock implying that the the string must be inclined at some angle however small the angle may be.