Burning The Ships

[Selmo]

Fëanor was mad, so it's not always useful to look for rational explanations for his actions.

In burning the ships, he acted on impulse, without thought for the consequences.
He saw himself as Super-elf, capable of taking on Melkor Morgoth on his own if needs be.
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[mormegil]

I believe the answer lies in the Curse of Mandos:

Tears unnumbered ye shall shed; and the Valar will fence Valinor against you, and shut you out, so that not even the echo of your lamentation shall pass over the mountains. On the House of Feanor the wrath of the Valar lieth from theWest unto the uttermost East, and upon all that will follow them it shall be laid also. Their Oath shall drive them, and yet betray them,and ever snatch away the very treasures that they have sworn to pursue. To evil end shall all things turn that they begin well; and by treason of kin unto kin, and the fear of treason, shall this come to pass. The Dispossessed shall they be for ever.
Ye have spilled the blood of your kindred unrighteously and have stained the land of Aman. For blood ye shall render blood, and beyond Aman ye shall dwell in Death's shadow. For though Eru appointed to you to die not in Ea, and no sickness may assail you, yet slain ye may be, and slain ye shall be: by weapon and by torment and by grief; and your houseless spirits shall come then to Mandos. There long shall ye abide and yearn for your bodies, and find little pity though all whom ye have slain should entreat for you. And those that endure in Middle-earth and come not to Mandos shall grow weary of the world as with a great burden, and shall wane, and become as shadows of regret before the younger race that cometh after. The Valar have spoken.

Bolding is my own.

Feanor's actions caused this Curse to come upon him and his followers. I don't think the question is why did he burn the ships as much as it's why did he begin? Everything after that is merely an afterthought or an effect of the cause. Feanor took upon him an unrighteous oath and was responsible for the kinslaying, he brought a curse upon himself and that curse influenced, if not dictated, all the outcomes of his actions.

Also there is this to consider:

But they [the Noldor] began to suffer anguish from the cold, and the clinging mists through which no gleam of star could pierce; and many repented of the road and began to murmur, especially those that followed Fingolfin, cursing Feanor, and naming him as the cause of all the woes of the Eldar. But Feanor, knowing all that was said, took counsel with his sons; and two courses only they saw to escape from Araman and come into Endor: by the straits or by ship. But the Helcaraxe they deemed impassable, whereas the ships were too few. many had been lost upon their long journey, and there remained now not enough to bear across all the great host together; yet none were willing to abide upon the western coast while others were ferried first: already the fear of treachery was awake among the Noldor. Therefore it came into the hearts of Feanor and his sons to seize all the ships and depart suddenly; for they had retained the mastery of the fleet since the battle fo the Haven, and it was manned only by those who had fought there and were bound to Feanor.

Feanor only knew one thing; get the silmarils no matter what the cost. His lust had rendered him so blind that if you had even one complaint against you he was willing to let you die. He is, in my opinion, similar to Cain from the Bible. He was the responsible for the first elf on elf killing and now that these Noldor were perceived to be of no use to him he left them to die. He deemed they would die too.

[Lindale]

Originally Posted by mormegil

Feanor only knew one thing; get the silmarils no matter what the cost. His lust had rendered him so blind that if you had even one complaint against you he was willing to let you die. He is, in my opinion, similar to Cain from the Bible. He was the responsible for the first elf on elf killing and now that these Noldor were perceived to be of no use to him he left them to die. He deemed they would die too.

I agree.

Also, when had Feanor not acted harshly and unjustly when he's so mad? I do not think he was humane enough to feel pity for those he wanted to leave, not after he slew some of the Teleri.