While rescinding something can be interpreted as undoing something, I think the key difference between the two words is whether or not the person/entity that is committing this action has the authority to do so.
For example, a government can rescind a law because it was the government that implemented the law in the first place. In other words, the government has the right to pass and abolish legislation. You or I cannot rescind laws since we lack the authority to do so.
In the above example the government effectively undoes one of its own laws. To continue on this train of thought, one can undo something without having the right or authority to do so. Let's say you're a fervent gardener and had spent the day on building a flower bed. I could simply come by at night and ruin it, i.e. undo your flower bed, even though I would have no right to do so.
So while your teacher does have a point saying that the two words are related, I would not go so far as to say they are synonyms.