I saw the enigmatic individual as essentially pitiless and cruel, as he was forced to be. I felt him as being beyond the pale of humanity, insensible to feelings of pity, the remorseless enemy of his fellow beings, against whom he must have sworn an undying hatred. (1.9.63)
Having known the captain for all of an hour, Aronnax already guesses that Nemo's hatred is what keeps him apart from man. This dude hasn't been banished in any traditional sense; he exiled his darn self.
Part 1 Chapter 10
I caught a glimpse of a frightening past in this man's life. Not only had he placed himself outside humanity's laws, but he had made himself independent, free in the strictest sense of the word, out of all reach! Who would dare pursue him to the bottom of the seas, given that he could foil any efforts made against him on the surface? (1.10.21)
One of Nemo's really big achievements is turning what would be a terrible, or, well, impossible place to live, into the perfect hideaway. Especially given that he's hiding himself away in a metal-plated warship that, as we have seen, can kick total warship butt.
The sea is nature's vast reserve. It was through the sea that the globe as it were began, and who knows if it will not end in the sea! Perfect peace abides here. The sea does not belong to despots. On its surface immoral rights can still be claimed, men can fight each other, devour each other, and carry out all earth's atrocities. But thirty feet below the surface their power ceases, their influence fades, their authority disappears. Ah, sir, live, live in the heart of the sea! Independence is possible only here! Here I recognize no master! Here I am free! (1.10.79)
Here, again, Nemo gushes about the freedom he's found in the sea. Whatever despot drove him there—and we're guessing one did by the way he loves to hate on the oppressors and donate to the oppressed—really blew it. This guy's perfectly happy living outside of society, thank you very much.
No man alive could demand from him an account of his works. God, if he believed in Him, and his conscience, if he had one, were the only judges to whom he could answer. (1.10.21)
Since his self-exile puts Nemo beyond society's reach, he's not subject to man's laws anymore. But Aronnax hopes that he will be accountable to both God and his conscience… the thing is, he's not sure Nemo believes in God, and he's not sure he's got a conscience, either.
Part 1 Chapter 14
Would I ever know to what nation this strange man belonged, that boasted of belonging to none? Who had produced the hatred he had sworn for the whole of humanity, the hatred which might perhaps seek a terrible vengeance? Was he one of those unrecognized scientists, one of those geniuses 'who had been hurt' to use Conseil's expression, a modern Galileo; or he was he one of those scientists […] whose career was ruined by a political revolution? (1.14.24)
As far as Aronnax is considered, Nemo's the latest in a long line of brilliant exiles: men whose genius got them cast out of society. What do you think?
Part 2 Chapter 1
There, not a single sea creature would come to trouble the final sleep of the inhabitants of the Nautilus, friends welded to each other in death as they were in life! "Not a single man, either!" the captain had added.
Always the same defiance of human society, wild and implacable. (2.1.1-2)
Nemo never considers returning to land, not even after death.
Part 2 Chapter 12
If I follow my hunch and if I have understood the captain's life, the Nautilus is not only a ship, it must also be a place of refuge for those, like its captain, who have broken all ties with the land. (2.12.13)
Nemo's not the only one looking for solace under the seas. He's a captain of exiles. He's a leader of wayward souls. We see this character trait in action off the Nautilus as well; Nemo's always defending and donating stuff to "oppressed" peoples.
Part 2 Chapter 18
I could understand how a life like this would suit a man who had no regrets about leaving life on shore, a Captain Nemo who was at home here, who went where he wished, and who pursued goals that were mysterious to others and known only to himself; but as for the three of us, we had not been made to break with humanity. For my part, I did not wish my intriguing and original studies to be buried with me. (2.18.7)
Aronnax and his buddies have no stomach for the whole "exile" thing, so Nemo's ship is less a refuge for them and more of, well, a ship—an awesome submarine ship. Aronnax's distaste for exile is really wacky, though. It's not that he's going to miss the old timey McDonald's, or anyone he ever knew; he just couldn't stand it if his scientific discoveries never gained him any fame.
Part 2 Chapter 20
What could be making him so unhappy? Was it being so close to European shores? Did he have memories of his abandoned homeland? In that case, what did he experience—remorse or regret? (2.20.39)
Maybe Nemo isn't totally over life on land after all? Arronax takes Nemo's moodiness as a sign of the fact that no matter how deep or far he travels undersea, Nemo can never escape the drama of land-based societies.
Part 2 Chapter 22
All these events passed before my eyes like minor scenes taking place in the backdrop of the stage. Then against this strange setting Captain Nemo grew out of all proportion. His character was accentuated and took on a superhuman dimension. He was no longer a fellow human, but a marine being, a spirit of the seas. (2.22.37)
All this time away from land and from other human beings doesn't just make Nemo an exile. It turns him into some kind sea creature. Our Captain, having so acclimated to the undersea life, and having been so consumed by his vengeance over all other emotions, becomes a kind of mythic beast: a spirit of the seas.