If there is something special about 35mm you haven't expressed it to my satisfaction yet.
If pressed, I would say that the following sentence says it in a nutshell: "It is about memory, desire, and yearning for completion."
My idea is that memory plays a more fundamental role with 35mm than with other formats, including digital, because we must accumulate "blindly" a certain number of pictures before seeing them.
Of course, you can accumulate quite a heavy stash of pictures with film like one does with digital, but where I think film is special is the forced delay between exposure and feedback. With 35mm, it's unavoidable that this delay be larger than one's memory of the events they photographed. With digital, regardless of how many pictures you take, you can always have immediate feedback. With large format, you still have a forced delay, but you don't have a whole roll to finish--most people will finish their 36exp before processing.
By the time you can see your 35mm photos, you have already forgotten quite a lot about them. They slip away from one's grasp, and printing them is like trying to reawaken deep memories.
But as the word "essay" means, it's only an attempt to say something, not the definitive word... Again, thanks for the reactions, of all kind, they are appreciated.