"Our teacher is not old."
It is unacceptable here. 旧 is generally for non-living things and 是 is not used in this kind of sentences; knowing whether or not something is suitable for a sentence, I think, is something that comes with practice and exposure to the language. However, if this is part of a longer sentence, it may be correct, e.g. 我们的老师不是老，而是善忘 or even when, for example, correcting someone, e.g. 我们的老师不是“旧”，而是“老”。 There are many ways to put this, these are what came to mind.