The man who really thinks he has an idea will always try to explain that idea.

I don't think that's the case. There are plenty of shy intellectuals who don't push their ideas on other people. Darwin sat more than a decade on his big idea.

There are ideas that are about qualia. It doesn't make much sense to try to explain a blind person what red looks like and the same goes for other ideas that rest of observed qualia instead of resting on theory. If I believe in a certain idea because I experienced a certain qualia and I have no way of giving you the experience of the same qualia, I can't explain you the idea. In some instances I might still try to explain the blind what red looks like but there are also instance where I see it as futile.

One way of teaching certain lessons in buddhism is to give a student a koan that illustrates the lesson and let him meditate over the koan for hours. I don't see anything dishonest about teaching certain ideas that way.

If someone thinks about a topic in terms of black and white it just takes time to teach him to see various shades of grey.