Why did Melkor mightiest of all the Ainur offspring of Eru's thoughts become discontented with his gift and seek more than what was within his power and authority given to him by Eru.
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So do all who live to see such times but that is not for them to decide. All you have to decide is what to do with the time that is given to you.
Quite simply, Melkor wished to create life of his own. "for desire grew hot within him to bring into Being things of his own" (The Si, Ainulindale). Essentially, Melkor's desire for power is what drove him to seek out a greater power (the Flame Imperishable), leading to his fall.
I see your point, however you have not pin pointed the exact origin of this desire. Why did Melkor grow to have desire for the Flame Imperishable as opposed to Manwe for instance?
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So do all who live to see such times but that is not for them to decide. All you have to decide is what to do with the time that is given to you.
Well I think this is the quote you need: But as the theme progressed, it came into the heart of Melkor to interweave matters of his own imagining that were not in accord with the theme of Ilúvatar, for he sought therein to increase the power and glory of the part assigned to himself. To Melkor among the Ainur had been given the greatest gifts of power and knowledge, and he had a share in all the gifts of his brethren. He had gone often alone into the void places seeking the Imperishable Flame; for desire grew hot within him to bring into Being things of his own, and it seemed to him that Ilúvatar took no thought for the Void, and he was impatient of its emptiness. Yet he found not the Fire, for it is with Ilúvatar. But being alone he had begun to conceive thoughts of his own unlike those of his brethren. (The Silmarillion, The Music of the Ainur) As you see, Melkor, just as Lucifer in the Christian tradition, became arrogant and envious and thirsty for power. You must also think that the Ainur were not all the same, they were all different, and had different qualities. So some went on Melkor's side, some didn't. Even thought Melkor and Manwe were brothers, they were very different and had different thoughts and ideas.
You have detailed exactly what I was looking for in this quote - I now realise as you say that the Ainur had thoughts of their own and as you say some went off on Melkor's path and others stayed with the path given to them by Iluvatar.
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So do all who live to see such times but that is not for them to decide. All you have to decide is what to do with the time that is given to you.
Well this also goes for the Maiar: "For of the Maiar many were drawn to his splendour in the days of his greatness, and remained in that allegiance down into his darkness; and others he corrupted afterwards to his service with lies and treacherous gifts." (the Silmarillion, Valaquenta) and also it goes for Men and Dwarves that also joined both sides.
Although I have brought this point up before, again I shall bring it up since something said earlier reminded me of it. Melkor had the desire to create life of his own and so went in search of the secret fire, the flame imperishable, as is understandable for one who's only next step to better themselves is to create life like their master (since Melkor was granted more power than all), but there was one other who also desired this Aule the smith, who desired it so much he created the dwarves but could not give them life. Aule was also the master of Curumo (Curunir/Saruman) and Sauron, he also taught Feanor who as great as he may have been used this skill to make the silmarils and then went on to kill his own kin because of them. Just a bit of food for thought from your friendly neighborhood istari. Just imagine how bad M.E. would have been if I had been corrupted by the ring!!
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...But it was so that from Nienna he learned pity and patience.
Olorin, there was one fundamental difference between Aule and Melkor though: humility. Aule was humble to the point of being willing to destroy his own creation if it displeased Eru, taking up his hammer to kill them. "Then Aule took up a great hammer to smite the Dwarves; and he wept. But Illuvatar had compassion upon Aule and his desire, because of his humility." (the Sil, Of Aule and Yavanna).
I would say that the fact Sauron, Curumo and Feanor became evil doesn't have to do with the fact that they had served Aule. For example Osse which is a Maia of Ulmo was also tempted by Melkor to receive "all the realm and power of Ulmo" (Valaquenta) And also for a time he did do Melkor's bidding. Also Radagast or Aiwendil as he was known, a Maia of Yavanna, also failed in his quest, "for Radagast, the fourth, became enamoured of the many beasts and birds that dwelt in Middle-earth,and forsook Men and Elves, and spent his days among wild creatures." (UT, The Istari) So as we see not only Maiar of Aule were enamoured by other things and refused to do the job they were assigned to. For example also Tilion, Maia of Orome, refused to remain where he should and he went on the pursuit of Arien. Of course the Maiar of Aule were a lot more likely to be enamoured by their creations, unlike maybe the Maiar of Manwe. But still it all had to do with the fact that they liked beeing creators and not with the fact they once served Aule.
Feanor did not become evil. He simply became so ruthless in his desire for HIS creation that sometimes he may have had to execute an Evil act, but this did not make him and evil being.