I have always wondered why Men and Elves are called the Children of Iluvatar (and he called Dwarves his adopted children), but the Ainur are not. Sometimes they are refered to as "children of his thought", but that is a different classsification. It seems to me that one possible explanation is that the Ainur do not have "free will" in the way that Elves, Men, and Dwarves do. Whenever there is a major decision to be made, they always consult with Eru before they can take action. Also, they themselves were the singers of the Music. It was said that they didn't fully comprehend the Music (and didn't understand the Theme that contained Elves and Men at all), but it seems to me that just in hearing the Music, they would be guided by it. Whenever something good results from the action of an Ainu, it is refered to as "doom" or "fate" or some such. Often, when the Ainur take action without consulting Eru, the consequences are undesirable.

I am not arguing that the Ainur are automata (my evidence doesn't come close to suggesting that), but I do think that they are not as free to choose their course of action as the Children of Iluvatar are. I think that this difference in the degree of "freedom" of will is why the Ainur and the Children are so often at odds. (One could argue that Men have even more "free" will than Elves, and that's the source of their estrangement.)