In our experience, we disassemble, repair and reassemble objects we can see and touch. Our goal is a repair. However, to repair today vehicles, we must expand our understanding beyond things we can touch, see and use wrenches on. We must apply the technician approach to learning, information gathering and analysis.
Suppose we bend our wire into a squarish, U-shaped loop so there are effectively two parallel wires running through the magnetic field. One of them takes the electric current away from us through the wire and the other one brings the current back again. Because the current flows in opposite directions in the wires, Fleming Left-Hand Rule tells us the two wires will move in opposite directions. In other words, when we switch on the electricity, one of the wires will move upward and the other will move downward.
Now we have better ideas about how electricity works, we tend to talk about current as a flow of electrons, from negative to positive, in the opposite direction to the conventional current. When you are trying to figure out the rotation of a motor or a generator, be sure to remember that current means conventional current and not electron flow.
If you are confused by me saying that the current flows from positive to negative, that just happens to be a historical convention. People like Benjamin Franklin, who helped figure out the mystery of electricity back in the 18th century, believed it was a flow of positive charges, so it flowed from positive to negative. We call this idea conventional current and still use it to this day in things like Fleming Left-Hand Rule.