Fëanor is an evil character. He's a villain. He's a necessary villain, certainly, a cool and interesting villain, a tragic villain, a villain quite unlike any other in Tolkien's writings. He's a fascinating and frustrating and tragic character, and he's absolutely the best-written villain in the Legendarium…but a villain nonetheless.

And it kind of bugs me that outside his own story, especially in LotR, he's always referred to in a positive light. Gandalf refers to “the unimaginable mind and hand of Fëanor at their work”, for example.

The core of his evil is very similar to that of Morgoth and Sauron - they're all absolutely, unquestioningly self-centered. And if Sauron was "only less evil than his master in that for long he served another and not himself", I'll say that Fëanor was only less evil than either in that he had only the powers of one of the Children of Iluvatar, not the powers of an Ainu, and so his means of satisfying his selfish desires were necessarily less directly destructive.

Throughout the Legendarium, Fëanor's chief fame is as a craftsman. He was also clearly a great leader and a powerful warrior, but his greatest achievements were those of his craft - the crafting of gems, the Palantiri, the tengwar alphabet, and, of course, the Silmarils. And there is what I see as a very, VERY important distinction made between other craftsmen and Fëanor.

Of Aulë:

Of the fabric of Earth had Aulë thought, to whom Iluvatar had given skill and knowledge scarce less than to Melkor; but the delight and pride of Aulë is in the deed of making, and in the thing made, and neither in possession nor in his own mastery; wherefore he gives and hoards not, and is free from care, passing ever on to some new work.

Of the Noldor:

And it came to pass that the masons of Finwë, quarrying in the hills after stone (for they delighted in the building of high towers), first discovered the earth-gems, and brought them forth in countless myriads; and they devised tools for the cutting and shaping of gems, and carved them in many forms. They hoarded them not, but gave them freely, and by their labour enriched all Valinor.

Of Fëanor:

though at great feasts Fëanor would wear them, blazing on his brow, at other times they were guarded close, locked in the deep chambers of his hoard in Tirion. For Fëanor began to love the Silmarils with a greedy love, and grudged the sight of them to all save to his father and his seven sons; he seldom remembered now that the light within them was not his own.

This to me is Fëanor's great flaw - he is greedy. Selfish. Concerned with what he saw as his own. He would disregard the work of others, and focus only on his own work or his own needs

I see people defend Fëanor's actions by quoting the line that

High princes were Fëanor and Fingolfin, the elder sons of Finwë, honoured by all in Aman; but now they grew proud and jealous each of his rights and his possessions.

Indeed, that line does indicate that both Fëanor and Fingolfin were guilty of this. But the essential difference between them comes in how they acted. In the same paragraph, we see what the 'rights and possessions' they were jealous of were:

Melkor set new lies abroad in Eldamar, and whispers came to Fëanor that Fingolfin and his sons were plotting to usurp the leadership of Finwë and of the elder line of Fëanor, and to supplant them by leave of the Valar.

And...

But to Fingolfin and Finarfin it was said: "Beware! Small love has the proud son of Miriel ever had for the children of Indis. Now he has become great, and he has his father in his hand. It will not be long before he drives you forth from Túna!"

It's what comes next that distinguishes the brothers: Fëanor makes the lies of Melkor true, while Fingolfin makes them false.

Fëanor shows that he has no love for the children of Indis, and he orders Fingolfin to leave Finwë's council, without the command or permission of Finwë; and further, he threatens his brother's life for an imagined crime.

For his part, Fingolfin simply says "I will release my brother"; he holds no grudge. Later, at the feast:

Fingolfin set at naught the unsheathing of the sword. For Fingolfin held forth his hand, saying "As I promised, I do now. I release thee, and remember no grievance."

Then Fëanor took his hand in silence; but Fingolfin said: "Half-brother in blood, full brother in heart will I be. Thou shalt lead and I will follow."

This is why Fingolfin is a tragic hero, and Fëanor a villain - Fingolfin seeks reconciliation. Fëanor seeks obedience. And despite the friction between the brothers, and despite Fingolfin’s own misgivings, he did exactly as he said - he followed where Fëanor led.

Alongside this interaction between the brothers, we have the parallel story of Fëanor's banishment from Tirion. Fëanor's reaction to this punishment is typically self-centred, and classic villain. Instead of, as Mandos said,

In that time take counsel with thyself, and remember who and what thou art.

Fëanor...well, sulks. He doesn't even consider that his own actions were wrong, and that those actions led to him being banished, he just considers himself unfairly treated and persecuted.

I have to admit, I hold Finwë to blame for a lot of this as well. His favouritism for Fëanor is rather sickening - he never lifted a finger to aid Fingolfin, his son, and sides with Fëanor throughout, even after the death threats. It would be easy to forget that Fingolfin was supposed to be Finwë's son as well, given his actions in this matter.

There's a lot more to say about Fëanor, and how his selfishness poisons everything he touches; but I don't have time to retell the entire story of the Silmarillion! Still, there's another pair of incidents I'd like to contrast.

The first is when the Valar ask for the Silmarils to restore the trees:

Then Manwë spoke and said: "Hearest thou, Fëanor son of Finwë, the words of Yavanna? Wilt thou grant what she would ask?"

There was long silence, but Fëanor answered no word. Then Tulkas cried: "Speak, O Noldo, yea or nay! But who shall deny Yavanna? And did not the light of the Silmarils come from her work in the beginning?"

But Aulë the Maker said: "Be not hasty! We ask a greater thing than thou knowest. Let him have peace yet awhile."

[...]

Then he cried aloud "This thing I will not do of free will. But if the Valar will constrain me, then shall I know indeed that Melkor is of their kindred."

Then Mandos said: "Thou hast spoken."

I don't entirely fault Fëanor for this decision. It was a terrible choice he was faced with. I think he chose wrong, of course, but I don't entirely blame him for that choice.

But what actually happened? The Valar did not command Fëanor to give them the gems; they asked. When one of them tried to pressure him, another stepped in to defend him. At the last, when Fëanor made his decision, they accepted it. What fairer treatment can we ask? And Fëanor declares that forcing someone to give up their treasure makes one kin with Melkor. Remember that, because we're on our way to Alqualondë.

But Olwë answered: "We renounce no friendship [...] But as for our white ships: Those you gave us not [...] the white timbers we wrought with our own hands, and the white sails were woven by our wives and our daughters. Therefore we will neither give them nor sell them for any league or friendship. For I say to you, Fëanor son of Finwë, these are to us as are the gems of the Noldor: The work of our hearts, whose like we shall not make again.

Fëanor presents Olwë with the same choice the Valar had just presented him. Not for the good of everyone in Valinor, though - only for the good of Fëanor and his followers. And when Olwë makes the same choice that Fëanor made, Fëanor uses force to take them.

Fëanor does exactly what he had said would show the Valar to be kin to Melkor. In this, he makes himself the kin of Morgoth as well - or at least, Morgoth’s tool.

One final point. The moment that I feel demonstrates Fëanor's place as a true villain.

At the end of his life, Fëanor sees Thangorodrim. And:

knew with the foreknowledge of death that no power of the Noldor would ever overthrow them; but he cursed the name of Morgoth thrice, and laid it upon his sons to hold to their oath, and to avenge their father.

Even here, at the end, when he sees that he has led his people to their doom, he remains utterly self-centred. He commands his children to do something he knows is impossible. He renews an oath that cannot be fulfilled, and lays a new charge on them that cannot be carried out. And he knows this.