TL;DR: Long term fans of the series seem to dislike this because it actually has a story. The truth is, the story and characters are what make it vastly superior to what came before.

I have played a number of Fire Emblem games. If you pinned me down, I couldn't tell you what the majority of them were about or any of the characters. Off top of my head, the ones I know I played:

Shadow Dragon (I actually have a limited edition of it. It's a terrible game.)
Shadows of Valentia
Path of Radiance
Radiant Dawn
Awakening
Fates
Three Houses <-- This review
Three Hopes (kinda counts)
Engage (ugh...)

The bottom three are clear. Any others are a blur.

Three Houses comes along, and at first I avoided it, but then relented. I'm glad I did.

What I Liked

✅ Fully voice acted, and the majority of them did an amazing job.

✅ Cutscenes aplenty, and lengthy ones.

✅ A decently engaging battle engine (when you get a certain level of powerful it starts to be less of a challenge, obviously).

✅ Supports that fully welcome full-blown relationships between characters. There's apparently a bit of tone down, but nothing as egregious as Engage.

✅ Decently accessible battle engine with predictable weakness/strength mechanics.

What I Didn't Like

👎 Women cannot fully be Grappler-type classes. Which makes no sense, because Leonie, for example, is amazing with gauntlets.

👎 The timeline mechanic doesn't allow you to take time fully appreciate each month segment. This is a similar feeling (but not quite as abrupt) as Shining Force. The result is that you feel like you're having to rush supports and searches.

👎 Every final battle feels grossly unbalanced compared to what comes before it.

👎 Certain of the paths feel unfinished or at least half-baked. Golden Deer (Claude), for example, doesn't really "resolve" like you might think, and Crimson Flower (Edelgard) has an intriguing story that cuts off way too soon. Verdant Wind (Dimitri) has arguably the most depth, but crams exposition at its end without context.

👎 To fully appreciate what's going on, you must play Three Hopes (where at least these three paths are expanded on, especially Verdant Wind). Three Hopes is a fine game, but it's unfortunate so much time was put into pointless fluff like "the Slithers" and not just having all of this context added to Three Houses.

👎 The DLC, Cindered Shadows, introduces a fourth House that never really feels 'integrated' into the rest. There are classrooms but no teaching, etc.

Summary

The above are nitpicks in the grand scheme. If anything, it's because of how good the game was that this is the result: wanting more from it vs. less.

Obviously, certain people dislike the added context and just want a bunch of fighting. Those games simply don't hold up especially now. There has to be more to it than just repeating the same thing over and over; and Three Houses does that for the most part.