Why did Owen Chase not fire his harpoon at Moby Dick?

It was supposed to show that after all that had happened, and all the crew who had died, he was able to resist as he realised the whale was fighting for its life in the same way he was.

Instead, he spares it and returns home, and is immediately horrified by how the whaling industry is behaving, glossing over the sinking of the ship and the crew's death to satisfy their own greed. In response to this, he immediately leaves the business to become a merchant sailor (a departure from the true story).

There are quite a few articles online from photographers and marine specialists who claim looking into a whale's eye changes a person's understanding of the creatures. For example, Bryant Thomas, a marine photographer, said:

...I saw for the first time the calm, mindful expression of a whale’s eye looking into my own eyes.

In that moment, she was completely transformed and was no longer a whale; that word suddenly became meaningless. In this overwhelming sensation of unfamiliarity, I saw clearly what had been missing in the thirty-five years of whale photography: intimate moments such as these documented at full scale and on the whales’ terms. Moments that reveal the calm, mindful gaze of a whale.

It's quite possible the film wanted to convey a similar sense of intimacy in the minds of viewers watching the scene.

Another reason that links in to this was the desire of the film-makers to not glorify whale hunting. To quote from an interview Chris Hemsworth gave the NY Daily News:

"We really wanted, were concerned to not have a pro-whaling movie by any means," star Chris Hemsworth recently told the Daily News.

"We wanted to depict the brutality of it, but also show some doubt and some remorse in what these men were doing, that this was the industry at the time."

I could come up with two reasons:

1. The Conversation between Captain Pollard and Owen chase about "Who are we to bend the rules of nature" some minutes earlier at the island... at the sheer overwhelming majestic sight of the whale, Owen stops to reconsider Cpt. Pollard's words.

2. He saw into the eye of the demon whale, while his last harpoon was still stuck close to it. He understood that he can't possibly kill it. And if he even tries, he'll risk all the little chance his crew and him had at surviving. It was also like a silent telepathy of the two strongest characters in the movie. He lets moby dick go, and in turn, the demon whale lets them be.

I haven't seen the movie, so I'm not positive if this matches the scene, but there is historical text documenting this encounter written by both Chase and cabin boy Thomas Nickerson. According to Wiki:

The whale rammed the ship and then went under, battering it and causing it to tip from side to side. Finally surfacing close on the starboard side of Essex, with its head by the bow and tail by the stern, the whale appeared to be stunned and motionless. Chase prepared to harpoon it from the deck when he realized that its tail was only inches from the rudder, which the whale could easily destroy if provoked by an attempt to kill it. Fearing to leave the ship stuck thousands of miles from land with no way to steer it, he relented. The whale recovered, swam several hundred yards ahead of the ship, and turned to face the bow.

I can only assume this is taken from Chase's account.

Well, Chase is an individualist hero. He pushes himself to win. Remember the scene where he cuts the line to free the sail. The white whale is Chase's opponent. He is chaos while Chase wants to "conquer the world" and presumably bring order and prosperity. Not unlike the epic of Jason and the Argonauts.

Later in the film, Chase changes. He asks "have we not offended God"? To which Pollard makes the argument that humans have dominion over the earth, citing Genesis. But the white whale isn't just a whale to Chase, or to us - the audience. When Chase prepares to kill the whale, he appears to think in succession that the whale is his opponent, but that it is allowing itself to be harpooned, that it is possibly incapable of dying, that he respects the whale, that it represents nature, that he wants to dominate nature, but that he respects it and draws from it, and thereby chooses not to kill it, gaining mastery over his own nature.

Well let's think about why the whale would come out to give chase such a clean shot to kill it when it knew very well that chase would most likely try to kill it.

I guess the whale might be dying a slow death already having been struck near his eye and wanted to be relieved of the pain and chase denied that easy death to the whale. When he figured that whale was doing the same thing to these men by not drowning/ killing them when it could have so easily done that all along the way when it was following them.