Multiple things could be said about the other routes, like how Azure Moon is all about blinding following an actual madman because he's the rightful heir to the throne, all while disregarding pretty much every other aspect of the world to tell the tale of poor boy Dimitri, or how Verdant Wind is written like a Saturday morning cartoon with a cool lord cracking jokes left and right and coming up with Pinky and the Brain level of schemes (when it's not his lazy retainer coming up with them herself), two feelings which seem comforted by the recent fan-translated interviews about how it initially was all about Silver Snow and Crimson Flower (Silver Snow which in my opinion is the closest route to make the most thematic sense, playing the tragedy card very well despite a number of shortcomings).
But I'll mostly talk here about Crimson Flower.
There are multiple key parts here but I think the reason I'm writing this all boils down to what Sothis says in an otherwise rather secondary cutscene, that she wishes for Byleth to carve their own path, choose their own destiny, something which obviously is only possible if you play Black Eagles.
That's kind of the keyword here. Byleth was a rather ordinary baby (their unusual mother notwithstanding) which would have been born dead if Rhea wouldn't have transplanted Sothis crest stone from their otherwise dying mother. From that point on pretty much everything is setup. Rhea while maybe not thinking about that on the moment (we'll never know that much detail it seems), quickly realizes it's another opportunity for her long standing "experiments" to continue. Obviously Byleth has no say on the matter and saving a baby can only be lauded, but what happens afterwards if what's interesting. She never tells their father what happened. Why the baby doesn't have a heartbeat. What she did so save them. She didn't even have to divulge her "experiments", she could simply have said she used a powerful crest stone to save them, problem solved, Jeralt never leaves the monastery. But she didn't. From the get got the child had multiple choices stripped out from them, being an ordinary human being, and knowing the truth about their extraordinary birth conditions. Byleth never has a choice expect to make a woefully uninformed choice of choosing which class to teach, something which in two cases out of three means they will never have to make another choice again. They will fulfill the destiny Rhea envisioned for their mother, even if it won't turn-out 100% like what Rhea planned (but we know she was doing rather blind experiments to being with, and wasn't sure herself on how those would turn out).
Which is why making the choice to disobey Rhea is so meaningful. It the one thing Byleth can do that his truly their choice. Following Rhea as Black Eagles leader is simply following what Rhea more-or-less planned to begin with.
But there's so much more to it than that.
I've seen numerous people argue about the timing of the choice, how it should have been "explained more", or how it should have been put before Edelgard's attack. But that's misreading a lot of things this game tells us. It makes sense for Byleth to try to stop Edelgard at first under the shock of the event, if only in the hope they could capture and interrogate her. And it makes sense that this choice is available when she is defeated (even if she still has a get-out-of-jail card to play). Rhea is the one asking you to kill her, reminding you that while she may not be in the position to give orders, she sees herself as in a position to give orders. Rhea embodies once again the powers that be. "Don't discuss orders, obey". And it makes sense that Edelgard would not ask Byleth directly for their help beforehand. She doesn't even ask for their help at that moment, because she's emotionally unable to. Every conversation up until that point hints to the fact that she would love Byleth to support her to the very end, but expects otherwise and as such rather prefers to "go with the flow" (of Byleth following Rhea) than ask and be disappointed by the answer, a rejection she knows she would struggle with.
It's also very interesting to note that a major, admittedly somewhat hidden theme of Crimson Flower is sparing enemies. In all of part one, you're never sent to capture bandits/rebels/whatever. You're the church literal death squads. And here Rhea asks to kill again. Without trial. Without even trying to interrogate what is basically her archenemies (or at the very least their allies) she can't get rid of for over a millennia. So choosing to spare Edelgard here can easily be read as "stop with the mindless killing".
It's important to note at that point that Edelgard clearly speaks of only attacking those who oppose her, and will offer surrendering to (almost) all her enemies during the Crimson Flower route, reminding us that she feels empathy, most likely because no matter what she suffered, she's still human.
And the game tells us how both enemies would react when driven back to their last stand. In Azure Moon, when Edelgard has utterly lost (or technically is about to), as TWISTED will not be dealt with by Dimitri and the Church will continue to be the dominant power on the continent, she performs unholy rituals upon herself, she turns herself into a daemonic monster in a last attempt to turn the tides, and when defeated commits suicide by Dimitri to avoid further bloodshed (knowing splinter cells would likely try to free her if she surrendered). In all routes but Crimson Flower (and also in CF actually, but it's not shown), Rhea "defends" the monastery by going full dragon rampage and demolishing most of it while fighting the imperial army, because she doesn't really care as long as she can lash out. And of course at the end of Crimson Flower, when she knows her very life or at the very least her dear religion built on lies is at stake, she burns an entire city because "why the fuck not". Because ultimately, she doesn't value human life, or maybe just doesn't value life for that matter, if only for the few of her kind left (she still sends them to fight though, so she likely only cares about her mother in the end).
Where I'm going there is that in all routes but Crimson Flower, it's all about being a force-of-nature (by sheer luck, as Byleth did nothing special to "deserve" the power of the goddess) who tramples the church's foes while offering little mercy opportunities, whereas in Crimson Flower it's all about leading a blitz as quickly as possible to minimize to number of casualties (that's one of the main point as to why this route is so short), all while allowing enemies to surrender/escape because you're still human despite borrowing the power of the goddess (a power you relinquish during the final cutscene, something which obviously echoes Edelgard stepping down from power at the end of the story, either because her lifespan was shortened, or because she simply did not actually want to become a "supreme ruler" but simply wanted to make the world a better place by reforming a faulty system, church included).
But it doesn't end there.
There are also meta-reasons as to why this route makes so much sense. It all boils down to the "every side is kind of right" theme and what IS woefully failed to achieve with Fates' Conquest campaign, which is to write a proper "bad guy" route.
Yes, you're technically siding with the Red Emperor (which should I remind you was almost always "right", if only for the fact that they declared war, and, as we all know, declaring wars is bad). And yes many things are questionable in that route, like how some of Edelgard claims are incorrect and how you're technically the aggressor and so the driving force behind the war horrors. But that's also why one of the first dialogs Byleth has with Edelgard is how her hand is shaking as she's starting a war and understands countless people will die as a result. That's why the tone of that route is so bittersweet; you know you're fighting for the right things but need to do horrible things to achieve such results. It's "Conquest done right". It makes you feel bad that you have to kill Rodrigue and Dimitri. It makes you feel bad that you have to crush Claude's dreams and send him back where he comes from. It makes you feel bad to see Flayn so disheartened that you chose to fight Rhea. But that's why it feels good. You're no longer the goody-two-shoes who always have the luxury of keeping the moral high-ground by being the heroic reactionary force. You're part of those who want to enact change and ready to suffer for it. You're not into some all-too-common power-fantasy of literally becoming the new local divinity, but are just a human with god-like powers who actively acts to relinquish said powers. Because as a wise man said, absolute power corrupts absolutely.
That's why it all works so well, it's what IS thrived (and failed) to achieve before, it's all about giving a broken person the wildest dream she's too afraid to ask, it's all about keeping our humanity in the face of overwhelming adversity, and it's all about breaking free from the shackles of fate. Remember why I started writing this? Something about Sothis asking you to choose a path that is truly your own? That's something you can do in Crimson Flower, and in Crimson Flower alone.
Thank you for reading.
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