Why didn't Balian ask for terms with Saladin before the siege of Jerusalem in Kingdom of Heaven?

I don't know what happened historically, but in the movie there are several aspects which tell us why Balian didn't ask for terms before fighting.

1. Saladin had already agreed to peaceful terms when Baldwin was the king. Saladin had come to invade Jerusalem initially because of the beheadings of Muslim caravan.

2. Later, Guy de Lusignan beheads Saladin's sister. It should be obvious that any one would be angry when they lose their dear ones to the enemy, especially after peaceful terms were sought.

3. Balian knew that Saladin would not agree to peaceful terms because more than half of the Christian force was dead and it would be a cakewalk for Saladin's army to gain Jerusalem.

4. Following the words of his father, Balian first serves the King of Jerusalem, Baldwin, and when after Baldwin's death Balian then serves the people of Jerusalem. So, for their safety, he decides to defend the walls so that Saladin is forced for more peaceful terms which are more safe for the people.

5. In the movie they have shown that at Saladin's camp, his chancellor Imad ad-Din asks Saladin for mercy and to leave the city, but Saladin refuses because of the anger of his sister's beheading and comments passed by his brother.

Balian did not think negotiations were possible. During his meeting with Saladin, he says that when the Christians took the city they massacred everyone in it and is surprised that Saladin would not do the same.

It's natural to expect that the Arabs will want revenge and given that the christian army was utterly destroyed, he has no leverage to negotiate.

I think he though that he'll either repel Saladin or die in the process.

By the way, I watched a YouTube interview with a history professor who wrote a book on that focused on the historic characters that the movie is based on - according to her, the dialogue between Balian and Saladin was pretty much taken word for word from the historic record.

My answer might not be correct, since I don't major in that part of history, so forgive me for viewing that plot from just my point of view.

The leader of Saracen, Saladin, lost hundreds of men at the wall and most of the siege towers. So, as being a calm and rational military leader, he could not risk more loss or the morale would probably fall. As long as he can take Jerusalem, taking revenge against Christian is not his motivation or at least not the primary one. And we can tell that Saladin is also a knight-like person in the director's view, imo.