I don't think explaining this using any reasonable, well thought out argument is going to do any good.
This man won't countenance defeat and therefore he will not listen. To listen is to be defeated.
He is invested in winning interactions with his daughter and with you. He is doing short term, minute by minute thinking. He does not care about anything but the prospect of losing the position he is building for himself in the family, which is 'He Who Must Not Be Challenged Or Questioned.' (Not 'he who must be obeyed', though that individual is a close relative.)
Any kind of challenge will be met with a fight to the death. You saw that when you and DD tackled him about it. He is not going to back down. He is not going to be reasonable. Please believe everything he effectively said about himself in that 'conversation' you had.
He went as far to say that he has no interest in empathising with children's feelings as it is not important.
He feels that she should accept his right to go in without knocking.
He is saying there is absolutely no appeal, on any grounds, that he will accept.
His attitude is similar in other contexts concerning our DC.
Would you be able/willing to provide a few examples?
So you need to stop talking and get a lock, or as many locks as it takes.
Get counselling for yourself (not couples counselling with him).
This crap has not developed overnight. You need to explore the dynamics of your relationship with this man.
Please do this, and don't be afraid of where it may take you.
You are dealing with someone who is not rational or reasonable. If you want to be driven literally nuts (seriously - it will affect you badly), start down the road of reasoning and appealing to his intelligence.