TL;DR: Never before has a gaming sequence polarized a community like Azure Gleam did with Three Hopes.

This post is to share why both sides got it completely wrong.

This writeup contains spoilers.  Do not proceed if you are bothered by that or have not played both games.

To understand: Three Houses had Azure Moon, and Three Hopes had Azure Gleam.

Azure Gleam is essentially an altered timeline; the events at the beginning of Three Houses essentially never happened.  That's where we must start to understand why Azure Gleam is basically near-perfect character development for Dimitri.

Kostas is tasked by "The Flame Emperor" (Three Houses)

In the main story, The Flame Emperor is presented as someone performing terroristic actions against The Church of Seiros, with no clear reason why.  The Flame Emperor recruited Kostas to trap and kill the noble students.

On one excursion, he's slaughtered a few  before encountering Dimitri, Edelgard and Claude as part of a training exercise.  Jeralt and Byleth stumble across the students and render aid, chasing Kostas and the others off to the Red Canyon, where he is chastised by The Flame Emperor for the failure.

Kostas doesn't know that Edelgard, the one he tries to kill first, actually is the Flame Emperor; and likely, Edelgard is either trying to get herself killed on purpose or didn't expect to be put in the position.

Kostas encounters Shez before encountering Byleth, as Byleth awakened early and helped kill Shez's fellow mercs (Three Hopes).

In this variation, the meeting with the Flame Emperor hasn't happened.  Shez kills Kostas, which causes Edelgard to change up plans.

Monica is rescued, rather than taken over by Kronya (Three Hopes).

Shez joins the Church and whatever house.  As part of an initial mission with Jeritza, Monica is located, locked up.  Monica, as told in Three Houses, went missing from the previous version of the Black Eagles when she was near graduation.

In Three Hopes, if Scarlet Blaze is the chosen path, a cutscene explains that Edelgard was trying to rescue Monica.  In Three Houses, Monica has already been replaced by Kronya.  This implies that in the Three Houses timeline, Kostas' failure and delay of Edelgard resulted in time being wasted where Monica got replaced before Edelgard could get to her.

What's not clear, is exactly how Edelgard knew where to look or why, other than vague cutscenes in Three Houses that implied that Edelgard was looking into "Those Who Slither In The Dark" behind the scenes, and had enrolled at the Academy to get more information about it.

Edelgard declares war on the Church of Seiros, and the concept of Crests in general (Three Houses, Three Hopes).

The one constant of both games is Edelgard's disdain for the Church.

The Holy Kingdom of Faerghus, descended from the Ten Elites, has always served to protect the Church that it is responsible for.  This meant Dimitri's purpose was already predestined.  But it is Three Hopes that finally explains what's really going on with him.

The Tragedy of Duscur was a conspiracy, where "Those Who Slither in The Dark" used a woman's sadness to gain power.  (Three Hopes)

Three Houses mentions the Tragedy of Duscur, but you don't really get much detail on it until Three Hopes.

The short answer, is that Edelgard's natural mother was sent to Faerghus along with Edelgard, to keep them safe from the "Insurrection of the Seven", a coup within Adrestia.  Patricia would fall in love with, and secretly marry, Dimitri's father the King.  This then made Dimitri and Edelgard stepsiblings.

During this coup, Thales (Those Who Slither In The Dark) saw a chance and took it, beginning to take over key members of Adrestia,  Faerghus and the Church (Tomas) in order to use influence to stoke war and dissension.  Patricia works to smuggle Edelgard back to Adrestia.  Cornelia, from Faerghus, worked to keep Patricia from going back.

What happens next is implied, never confirmed:  Patricia convinces Faerghus generals and mercenaries, as well as the King, to ignite the Tragedy of Duscur as a distraction while she tried to escape, then presumably died in the conflict.  Cornelia would imply that Edelgard killed her; but that would have been impossible.

Three Hopes (Azure Gleam) reveals that Dimitri's sole reason for coming to the Monastery when he did was to solve the Tragedy of Duscur.

Part of this discovery is to also understand what happened to his stepmother, which is when Cornelia implies that Edelgard was the one that killed her.  In fact, Cornelia's statement could be interpreted as Edelgard having at least started some of the flames that day.

But the key difference that many people missed about Dimitri in Three Hopes vs. Three Houses:

Three Houses Dimitri was "damaged" by what happened, specifically, that Edelgard was the Flame Emperor, the cause of so many deaths, and only realized the truth at the very end.  Three Hopes Dimitri was not, because he realized early on that Edelgard was just another victim, but still had to be stopped.

It is this that presented an amazing ending conversation.

In Three Houses, after beating Hegemon Husk Edelgard, Dimitri reaches out one last time to try and help her; but he's not offguard.  Edelgard throws the dagger that was once the gift given to her by Dimitri back at him and hits his shoulder at the same time Dimitri stabs her to death.

It's a sequence that says, "last chance to go back", and Edelgard not accepting it.

The problem with this sequence is simple.  If Edelgard was still under the influence of "Those Who Slither In The Dark" at this point, she was already behind any help that Dimitri could offer; and he knew that from Hubert just before.

It's an ending designed to be tragic, but completely undermining the "big bad".

In Three Hopes, if you recruit Byleth, you enter a side 'dream' sequence with all three House leaders, and it is here that Dimitri and Edelgard share a moment; but Edelgard, recognizing who Dimitri is for the first time, basically brushes it aside as the past.

The problem with this specific sequence is that it's completely disregarded after leaving this space, and it's like nothing ever happened (thus why it's referred to as a 'dream' sequence).  Edelgard is still under Thales' control the entire time, he just can't directly influence her without being in close proximity.

Three Hopes sees Edelgard basically being constantly revived and controlled like a puppet on a string by Thales, until finally both are put down.  Edelgard is now stuck in a childlike state, asking for "Dee" (the childhood nickname for Dimitri), who turns and walks away.

This sequence has only one real problem, which is the lack of explanation of the childlike state.  But we think it's a bit deeper.

Suppose Edelgard has gone blind at this point.  Her gaze is off in the distance and not specific, and she hears a voice she recognizes.  Which implies her memory has returned but it's been wiped back to some point before she returned to Adrestia.  The experiments done on her may have created a dissociative personality disorder - that basically she "died" once the experiments started.

Many online disliked this ending because they wanted Dimitri to embrace her or something.  But why?

Consider:

• Edelgard started the war.
• Edelgard slaughtered countless people as part of the war.
• Edelgard might be responsible for the death of her mother.
• Edelgard might have been indirectly responsible for the Tragedy of Duscur.
• Edelgard was indirectly responsible for the death of Jeralt (Three Houses).
• Edelgard was indirectly responsible for the death of Rodrigue (Three Hopes).
• Edelgard's alliance with "Those Who Slither in The Dark" (Three Houses) was done on purpose, not accident.  She was using their power to try and take down the Church.

It didn't really matter whether she was or was not under control.  As a King, Dimitri had a duty, and the people mattered more than feelings at that moment.

In short:

There was no compelling reason for Dimitri to have any positive feelings about Edelgard whatsoever.  She was not the same person he knew when they were younger.  It would make no sense other than to make people smile - but those people miss the point about why Three Houses and Three Hopes are arguably the best in the series:

They're tragic.

You're not supposed to smile at Edelgard or feel bad for her.  You're supposed to feel bad for the world she helped decimate and the countless people she killed directly or indirectly.

Three Hopes helped tie up loose ends that reaffirm Dimitri as not a man pining over a childhood crush, but a King that must see to his people first and foremost.  It corrected the mistakes of Dimitri's character in Three Houses, as someone that feels bad for a murderer.

It must be said.

If Edelgard were a male doing the exact same thing...the reaction online would be completely different.