I think that proverb is pretty profound.
Basically it’s saying you cannot reason with somebody who is being unreasonable. You cannot reason with somebody who does not care about the truth, who is willing to ignore facts, evidence and the truth in favour of continuing in whichever belief they prefer.
Because I care very much about the truth and what is true, it is one of the most frustrating parts of dealing with otherwise intelligent people who claim to be religious. There is no reasoning with somebody who is acting stupid, who is forcing idiocy on themselves. Presenting facts and evidence to somebody who flat-out refuses to see it is a pointless and frustrating task.
Having said that, it’s becoming more difficult (in the developed world anyway) to pretend to be asleep. Knowledge and information is so easy to come by now that you have to work much harder to ignore it than before, which is why the global atheist movement is growing so fast. That’s my opinion, at least.
There is another saying that’s similar which says you can’t reason somebody out of something they are not reasoned into. It’s true I think. You don’t reason somebody out of the religion they weren’t reasoned into. You present the facts and hope that eventually they pull their head out of their arse and see the light. Metaphorically speaking of course.