If cultural relativism were true, then ...

1. we could no longer say that the customs of other societies are morally inferior to our own. (P 379b)
2. we could decide whether actions are right or wrong just by consulting the standards of our society. (P 380b)
3. the ideas of moral progress and social reform would be meaningless.

But many of us are unwilling to accept these consequences.

So by modus tollens we conclude:

Cultural relativism is not true.