-Should a DM throw his player into an unwinnable battle against such a tough opponent?
I would answer that in general, "No." Unwinnable battles generally aren't fun for either the player or the GM and are to be avoided, and that if you do construct such a scene there should be a way to opt out without a lot of cost by the players and you should have as a GM a back up plan to end the fight quickly with little cost should the players be stupidly valiant.
That said, there have been plenty of battles that my players have constructed through their actions that I never intended for them to get into, and I don't feel a notable impulse to protect the players from their own stupidity. For example, I had one near TPK occur because in the midst of a combat, one party member decided to start looking for treasure that he could filch while the other players were distracted, which resulted in him triggering a second encounter while the first was on going, and then - not content to wreck things for the group to that extent - he proceeded to thrust open a sepulcher looking for further treasure which triggered a third encounter simultaneous to the first two. That sort of thing isn't my fault, and while it sucks for the rest of the party that was engaged in intelligent non-selfish functional play, you can bet that the reckless chaotic stupid PC is going to be the first character plausibly torn apart as a result with no real fudging on my part. Those sort of problems tend to be self-correcting in the long run.
I'm not saying that the DM should never railroad a party in order to avoid an action derailing a campaign, but it really should be used sparingly and mostly with new and inexperienced players. Taking away player agency to keep the game going in the long run destroys the game anyway.
At this point we really don't know how this encounter came about, so while it is likely the DM constructed it (and should learn a lesson about assuming PC behavior) we can't really say for certain that the DM is acting badly in any fashion here.
Should the DM offer such a cruel ultimatum as a way to survive?
This question I consider to be highly flawed, because the DM is not the dragon. The first question was about the metagame and the sort of scenarios that the DM should design, and that is properly a question about the DM. But the DM did not offer such a cruel ultimatum: the dragon did. And if you can't keep that sort of distance between the NPC and the DM, it's.... worrisome. PC's aren't their players. DMs aren't the NPCs.
The real question is, "Should the dragon offer such a cruel ultimatum as a way to survive?"
And the answer is, "Well, it certainly seems reasonable for a dragon to do that." While my dragons are bit more incarnations of violent forces of nature, I do take a lot of inspiration from Tolkien and Tolkien's dragons are rather more explicitly diabolical in their nature and as such are tempters and deceivers that relish degrading and negating what is good. The sort of Faustian bargain that the dragon presents the PC in this scene is I think very much in keeping with the interaction between Glaurung and Turin in Tolkien's 'The Silmarillion', where the dragon is not interested in killing Turin but rather in ruining Turin. So it's entirely in keeping with the interests of a diabolic dragon to try to get a Paladin to break their oath, because a ruined paladin is more interesting than a dead one.
To the extent that the DM's preferences are involved in this, I can see this sort of thing being offered up as a sop to a character that has played themselves into a stupid corner and you are trying to let them get out of it in a way that can ultimately be repaired. There is some suggestion that the DM had planned for the PC to come out of this encounter alive no matter which way it went, and that's fairly strong DMing technique. And as I said, I don't think you should set up situations like this, but what the DM is doing here is a very strong technique for getting out of these sorts of situations.
-Should the DM punish the player for choosing to live to fight another day? (but abandon the npc in the process)
And again, this question is highly flawed. Nothing suggests that the DM is punishing the player, and if you think that is the case then... yeah how do you even manage to play an RPG with a social contract like that? "Bad things happen to my PC, therefore you are punishing me.", is such a dysfunctional table logic that I can't see how you manage to play a recreational RPG together. If bad things happen to your character do you take that as some sort of personal attack on you? I just don't get it.
The proper phrasing of this question is, "Should whatever powers that hold the Paladin's Oath cease to have a relationship with the Paladin, that is cease to grant him power to use on their behalf, in response to the characters action?" This is a question about what is going on in the game, and not a question about what is going on outside the game.
And again, if you look at this question from the perspective of what is happening in the game, it's entirely reasonable that whoever this Oath of the Ancients was made to consider this a deep violation of the sacred trust and just ends the relationship.
The real question that involves the preference of the GM and the player, is where do you see this going next? How do you want to take this character in the future? Do you want to abandon this character? Do you want to redeem this character? Do you want to take this opportunity to make an alignment change, or a change in character to make a character that is more like what you want to play? How is the PC going to react to this situation? What sort of story path should I be preparing for, and how I can help you mechanically deal with this loss of Paladin powers. Do you want replacement powers? Do you want to play out a more penitent role even if that means at least temporarily disempowering your character?
And as long as you stay focused on that, this isn't going to turn into a table argument with a bunch of hurt feelings and recrimination and shouting and so forth. The story might not have gone where everyone wanted it to go, but it's still a strong story and there is a lot of opportunity to do cool things with it going forward. And that's really the 'hat' the GM should be wearing once he takes off the referee hat here. Forcing the GM to put on his 'arbitration/judge/leader' hat and hear some sort of OOC argument here, which from what a lot of people are saying in this thread even removed from the situation is going to be quite emotional, is just not friendly mature play by the player.
A private discussion that you don't feel the situation was fair after the game might be in order, but a lot of what that discussion is going to sound like if I'm the GM is going to be, "I hear your pain. I've been in similar situations. But I'm not the dragon or your deity. I have to play those characters plausibly to the setting or there is really no point in playing the game because it won't produce anything worthwhile. I'm not punishing you. I've got no desire to stop this story, so the worst thing from my perspective is if you just feel you need to abandon the character or the game. But I'm not going to sacrifice the integrity of the game either, because we then might as well abandon it. If you feel you are being punished unfairly, direct that complaint to your deity in game. That's a great scene with a lot of literary value and allusions you can draw upon to create really meaningful RP. If you want revenge on the dragon, talk to the other characters in character about directing the game in that direction, and I will as GM facilitate that."