Without first hearing the definition of "opposite" your teacher uses, or hearing examples he's used, it's difficult to select the proper argument. So he may pull semantics on you. However, here's some potential ideas:
Omnipotence - the opposite cannot exist. The very existence of anything means that has an effect, and is therefore a subset, not the opposite, of omnipotence. The only thing that can be opposite is something that has zero effect, in other words, is non-existant. But that's a paradox your teacher can't argue. (Except to argue that omnipotence doesn't exist, which is true, but the IDEA of omnipotence exists, and cannot be an opposite idea of omnipotence can not for the same reasoning.)
Stinky (no "pleasant" is not an opposite, it's just different) Tell him to provide a smell that is the opposite of "lemon", and you'll concede the argument!
Any word (Not what the word defines, but the word itself)
Any date - no, the BCE/AD eras are just arbitrary way points, and he can't go back before the beginning of time, because by definition, there is no date before the beginning of time.
A snowflake - make him prove otherwise)
Don't let him use the anti-matter argument, because he can't prove that there is an anti-matter opposite of the actual sample you select. Also, anti-matter does not cancel or oppose matter into oblivion when they meet, they convert to another form - energy.
An idea. There are only different ideas, not opposite ideas
Don't let him use zero or absence as an opposite. An opposite is generally defined as an opposing and cancelling condition, and zero opposes nothing. Which is also why vacuum is not the opposite of matter. Vacuum doesn't cancel matter, so is therefore not the opposite of matter.
Which is also why good has no opposite, only degrees of presence, if you define good as the absence of bad.