One of the most enjoyable parts of Fire Emblem: Three Houses is watching the characters in the game talk and grow together. Once two characters have enough affection for each other, their relationship improves after they talk in a support conversation.
Sometimes, the duo easily meshes with one another. Of course, any relationship has its bumps in the road, but characters can usually get past their differences and come together. A lot of the supports are cute and end with the duo discussing marriage in some form or another. There are some relationships that work, and others that just don't no matter how cute their support conversations are. **Spoiler warning for the different endings of Fire Emblem: Three Houses**
10 Makes Sense: Edelgard & Lysithea
These two make quite the pair. They are both intelligent, motivated, and mature for their age (even if in Lysithea's case it's sometimes a facade). Edelgard is determined to help Lysithea survive because Edelgard went through the same thing Lysithea did. They share a goal: to make sure no one else has to go through what they went through.
They are connected through their mutual pain and work hard to overcome the obstacles in front of them. They are a pair that work well together. Lysithea devotes herself to helping Edelgard, and, in return, Edelgard rewards Lysithea with cake.
9 Doesn't Make Sense: Blyeth and Sothis
This one is strange because of the nature of the duo. Sothis and Byleth become one in every route, so in a sense, Byleth would be dating his/herself. It would be like dating someone that no one else could see.
Besides the fact that Byleth and Sothis are one, Sothis constantly berates Byleth. Sothis, being a god, sees Byleth as a lower form of life at the beginning. She treats Byleth like a child and never seems happy to be stuck inside Byleth. She complains a lot about being in Byleth; meanwhile, Byleth doesn't do anything to prove her wrong.
8 Makes Sense: Claude and Petra
Despite being in different houses, these two are both in similar situations. They are both the only outsiders in the Academy. They both come from places that have problematic relations with the countries of Fódlan. They both wish to fix these relations, they have similar goals in mind.
The duo is devoted to their goals and their homes. They want a world in which their homes and Fódlan live in peace, and together they strive for that peace. Also, they both like taking naps outside which is a plus.
7 Doesn't Make Sense: Hanneman and Manuela
These two constantly are bickering with one another. At the end of every single one of their supports they argue. Sure, they make up, but that doesn't make the relationship as a whole better. If they were to work, they would constantly have to watch their tongues. A relationship that is built on fear of an argument is not a relationship at all.
Also, Hanneman's obsession with Crests could be a bad thing in the relationship. His work seems to always come first; meanwhile, Manuela seems like the type of person who would want a good amount of attention in her relationship, which is why these two don't work well together.
6 Makes Sense: Dimitri & Dedue
These two have been through it all together and are insanely devoted to the other. Dimitri saved Dedue, and Dedue lives his life to protect Dimitri and carry out his will. Despite this, they have a very good relationship. Dimitri never takes advantage of Dedue's devotion to him and constantly reminds Dedue they are friends.
To Dimitri, Dedue isn't just his shield. He is a trusted friend and ally. Dimitri is also the only person who doesn't believe that Duscur caused the Tragedy of Duscur. These two trust each other so much, and it is difficult to picture them with many other citizens of Fodlan.
5 Doesn't Make Sense: Byleth & Rhea
Rhea doesn't deserve Byleth, simple as that. Mistakes can be forgiven and usually forgotten, but Rhea failed Byleth. Rhea was the reason Byleth's mother died because she was willing to do anything to bring back her own mother. While it was a noble goal, it doesn't change the fact that she killed Byleth's mother. When Byleth became a professor, Rhea lied to Byleth time and again despite claiming to trust him/her.
Not only that, but Byleth is Sothis. Sothis is Rhea's mother. If they are together, Rhea would be sort of dating her mother. While it's true they are basically gods, it doesn't make it any less weird.
4 Makes Sense: Lorenz & Marianne
So this one may sound strange since Lorenz is Lorenz, but these two actually work well. Lorenz is fixated on beauty and shallow qualities, but the way they interact shows he doesn't feel that way with Marianne. Marianne thinks little of herself, but Lorenz thinks she is something special.
Lorenz doesn't really even try to change her. He claims that she is beautiful just the way she is. He finds her beauty is on the inside, which is a change from his usual desire for beautiful women. Lorenz brings out the best in Marianne, and Marianne brings out the best in Lorenz.
3 Doesn't Make Sense: Bernadetta & Raphael
These two don't work because of who they are. Bernadetta can best be described as a scared mouse that doesn't want to go out. Raphael is a bear who wants to better himself and protect others. He is loud, boisterous, and likes to go outside. All things Bernadetta is not.
Bernadetta is easily frightened, and Raphael is a loud guy with huge muscles. Raphael doesn't mean to scare Bernadetta; it's just in his nature. Still, just because it doesn't make sense doesn't mean it can't work.
2 Makes Sense: Byleth & Dimitri
There's a reason why Dimitri comes back to the light in the Blue Lion's route, and that reason is Byleth. Dimitri's need for revenge is what causes him to forget his friends and leave them behind. He refuses to talk to anyone or try to change. And when he finally wants to change, he doesn't believe he should be given the chance. That is where Byleth comes in.
Byleth was always there for Dimitri but never forced him to change. S/he lets Dimitri change on his own and is there for him when he needs it most. Without Byleth, Dimitri couldn't change because he needed someone to lean on. Byleth brings out the change Dimitri needed to become a leader Fodlan needed.
1 Doesn't Make Sense: Gilbert & Any Student
First of all, it's weird. He's the oldest character (excluding Rhea and Sothis) in the game, making him about three times the age of most of the students at Garreg Mach. Of course, age isn't the only thing.
Gilbert abandoned his daughter and wife to pursue his career. Sure, he makes up with them in the Blue Lions route, but who's to say that he doesn't do it again. He has issues with attachment and put his duty above his family. He doesn't really have anything in common with the students due to his age, so it's unlikely a fruitful relationship could blossom between him and one of the students.