My headcanon is that Melkor had great aspirations and dreams and ideas, and in the great Song he wanted to sing the way he wanted. But being denied all of that, his aspirations were twisted into darker thoughts and that is where his envy comes from. He then Went on to pursue his Dreams, but his Dreams were now different — he still wanted to create his own things, rule according to his own will, but he did it all to anoy Eru. His Dreams, however, are what made him create all his monstrous minions, what made him call himself the creator of the World, and claim that Eru did not exist after all.
Of Eru and Melkor
"Why have you made us?" they asked, looking at their Creator with a mix of love and fear.
"I wanted to create something of my own, something into which I had put my own thought, so that I could see it live and love it," said He. "And therefore I needed something that would guard it in my absence, so I created you, yet even you are the offsprings of my though."
They all had gathered around Him, around Eru. Closest to Him on his right side sat Melkor and on His left side sat Manwë, brothers, both dear to Him, (though one maybe a bit more so).
Brothers, but so very different. Melkor was more talented, more inquisitive, whereas Manwë was more kindhearted and more obedient.
"The Secret Fire powers you and its energy shall create Eä," He said.
"Can we use it to create something?" asked Melkor (sounding interested).
"The Secret Fire is not for you to use, and I have hidden it from all Eyes. It shall only be used indirectly to spring Life within Eä."
(Had He now spared a glance at Melkor, He would have noticed a scowl. But He did not.)
"What is it that you wish for us to guard, Creator?" asked Manwë as he bowed before Him.
"You shall guard my Children. My Children who shall be born in Arda in which those of you who go there shall rule with Love and Justice."
"Will you not guard your Children yourself?" asked Melkor (now sounding surprised and a bit disapproving).
"I am the Creator," said He (ignoring Melkor), "and you are my vassals. Will you serve me?"
"Yes we will," they said. "For the kindness you have shown us, we will serve you however we may."
"How will we serve you," asked Melkor (refusing to be ignored), "if we cannot even create anything."
"You will serve me in other ways. I cannot let you wield the Secret Fire, for that flame is a dangerous thing in the wrong hands, but —"
"If you created us, how can our hands be more wrong than yours?" asked Melkor. (No, not asked, questioned Melkor. He was questioning Eru himself. And he was interrupting.)
"Not even my own Creations such as yourself can escape corruption," said He in reply.
"What is corruption?" asked Manwë, for he did not understand such concepts, being pure of mind (and believing others to be the same).
"Corruption is that which mars all things good," was His explanation.
"Who created corruption?" asked Melkor.
"No one."
"Can I create corruption?"
(A moment of silence. Here Eru would have frowned, but he refrained from doing so.)
"Or do I need the Secret Fire for that, too?" asked Melkor. (Spitefully. Spitefully! How outrageous!)
"We do not want to create corruption," said Manwë to his brother. "Why should we mar all things good?" He looked at Eru with puzzled eyes. "If my brother creates corruption, will I have to destroy it, even though it is something created by my own brother whom I love?"
"Especially if it is something created by me that I love," added Melkor. "You said Creation is something into which one can put their thought and then see it live and love it, too. Surely something created by us should be as much worth as something created by our father?"
(From somewhere behind them Aulë said something in agreement, but sweet Aulë, you were never supposed to think like that! It is selfish.)
"Only if it is something I have approved of. I permit you to rule, but only according to my will." (Here He elegantly avoided answering the question of Manwë.)
"What is your will?" asked Manwë.
"What is our will?" asked Melkor in turn. "Do we even have our own will?"
"How do we know your will, if you do not join us in your Arda?" asked Manwë (now confused).
Brothers, but so very different.
"Manwë," their Creator addressed the Ainu sitting by his left side. "You shall follow my will, and if my will is that you destroy something that is corrupt, then you shall destroy it."
(Manwë looked concerned and glanced at his brother as if expecting Melkor to sprout out something corrupt at that very moment, but He ignored it.)
"Do we have a free will?" Melkor insisted (looking fierce). "I have a free will. I have a free will to (just like you) create something of my own, something into which I can put my own though! Why cannot I have the Secret Fire?"
"You cannot."
"But why?"
("Because I said so," their creator thought, and wished for a moment he hadn't given them free will. But of this he said nothing. Instead: )
"You are my servants and you are also the servants of my Children. These are your duties."
But Melkor had stood up and risen into his full might, and he looked terrible in his anger as he looked up at Eru and declared: "Why then do I have a free will, if I am to be merely a servant?"
(There was a collective gasp among the others at such outspoken thoughts, but Eru remained calm, because what could Melkor possibly do? He would never find the Secret Fire. No one would. No one could.)
"Melkor, you are the mightiest being that has sprung from my thought, but you are also proud; indeed, to proud for your own good. But I am the sole reason you exist, so you should not scorn me."
For a moment their eyes met. Then Melkor finally bowed his head (but only slightly).
"You are right. I am proud (but so are you); I am selfish (but so are you); I am wrong in wanting to create something of my own to rival that which you have created (though I would create something for the same reasons as you). I am a lesser being than you (but I am also the being with the most power and might next to you). Forgive me (and maybe I shall forgive you)."
At these words He said nothing, but then Manwë rose up and spoke in his turn: "Forgive my brother, for he is dear to me as only a brother can be. I wish for no grievance (for it frightens me); I only want peace (as I always have and always will). My brother is strong and maybe too strong for his own good, but he means no harm (for why would he?).
Brothers, but so very different (and He was beginning to change his opinion of which of the two was his favorite). They stood in front of him, side by side, but whereas the other was filled with love and compassion, the other was filled with bitterness and envy.
("You think that we are not so different, you and I. Are you arrogant or are you right?" thought He as he looked upon Melkor, but He said nothing. Instead: )
"I hear your words, Manwë, and see that your mind is kind and pure. Melkor shall be forgiven."
The Ainur were glad at the news and rejoiced and thought of it no more. (But He knew that Melkor was not content.)