You must, therefore, pardon the freedom with which I demand your attention; your feelings, I know, will bestow it unwillingly, but I demand it of your justice. (Chapter 35)

I think the letter is quite Darcy-centric; it is all about him. The only apology he offers is that of stating opinions which will offend Lizzy because they must be said and that of demanding her attention. No apology for the manner of his proposal. No apology for misleading Bingley about Jane’s feelings for him. Darcy’s goal is solely to redeem his character with Lizzy and the idea that he has a right to do it despite Lizzy’s feelings is central to his thinking. It reminds me of his confidence in Lizzy’s acceptance of his proposal. Darcy may have been stung by Lizzy’s rejection and her accusations but he is far from apologetic for his previous actions. I do think his desire to set the record straight is both natural and worthy although the manner of his obtaining justice imposes on Lizzy which his actions show he is well aware. His writing a letter and giving it to her is in itself inappropriate. Should anyone find out about it they would certainly think their relationship was more intimate than it is; that they are engaged. To avoid anyone knowing of the letter he stands about in the park till he can give it to her without anyone as witness. That he writes it and Lizzy accepts it shows they both are willing to skip the proprieties when they want to, he wants to clear his name and she is extremely curious. I think Darcy’s need to write the letter also illustrates the fact he still thinks very highly of Lizzy. He does not want her to believe he is dishonorable and cruel. His telling her of Georgiana’s almost elopement shows that he trusts her a great deal and IMO Darcy is actually upping the intimacy (unthinkingly IMO) of their relationship by revealing his actions towards Jane and Wickham. I think his apologies to Lizzy for stating unpleasant opinions shows he has learned at least to think of how his honesty is hurtful, even if it does not prevent him from saying it. ;D