Use this phrase to prepare listeners for something you're going to say. Common adjectives to use in this expression are:

This might sound crazy, but what if we opened the show up to the general public and sold tickets to it?

This might sound harsh, but I say we kick him out of the apartment if he's late with another payment.

This might sound stupid, but can't we just go up to him and ask him directly?

So you use this kind of phrase by thinking of what negative adjectives people might think of, and then saying "This might sound ___, but..." When you do this, the listener can't complain as much about what you said because you've already admitted that it might be sexist, crazy, harsh, and so on.