I see now. Your instructor is not wrong--they are just acting on two assumptions that you aren't yet familiar with.
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One is the basic mechanical limitations of dancing with a partner. When making a forward step in closed position (which is the likeliest way to proceed, given the set of steps you describe), you cannot turn right on a left-foot lead, and you cannot turn left on a right-foot lead. The reason for this is pretty simple: your partner's leg is in the way!
Try turning right on a left-foot forward step with a partner and you will immediate notice the problem (be careful not to kick them too hard). In order to execute, you'll need to transform the forward step into a sidestep, which DOES provide the space to turn right.
As for stepping right with the left foot (as opposed turning right)? In closed position, your own leg is in the way. In order to do this, you need to cross your thighs and step across your body, which requires you to rotate your hips. And in order to have that twisted hip position, you and your partner must be in Promenade or Outside Partner position...which requires a step or two to set up.
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Two is the general principle of respecting the line of dance (LOD). After the steps you mention, I am facing in the direction of the LOD. There is nothing mechanically preventing me from deciding to reverse course and step backwards with my left foot, but it is quite rude to the dancers behind me, and so is strongly discouraged. Stepping sideways towards the center of the room, by contrast is OK. Naturally, continuing forward is also OK.
Hence, I think, why your instructor says you "cannot" step backward. You can--it's just that you shouldn't, and they are trying not to overload you with information.