Time for Tvtropes.
Why on earth does Sumia have the knight class? It's the only class with a tripping animation! Whenever you try to use Luna or something to that effect as a knight or general with a lance, you will run past them and fall over. Not to mention, a Knight/General has high defense and they're good to protect weaker units; af asked about her free time, Sumia says she "makes sure everyone's safe" — this means, the Knight reclass option will allow her to protect others better, even with her own body/armor if needed!
Not to mention, Sumia didn't get her Pegasus until the chapter in which you can officially control her. Yet she was obviously a part of the Shepherds before then... It's entirely possible that she would have been a Knight instead.
Some of the Second Seal reclassing options may seem filler or out of the blue for the character in question, but some do make sense after learning of their background:
Why does Henry, a magic user, have Barbarian/Berserker as a reclass option? Because he's Ax-Crazy, geddit? (And the bad pun fits his character)
But Wait, There's More! Henry's supports with Ricken and the second Drama CD state that he had an Odd Friendship with Mustafa aka the boss of Chapter 10, who treated him like a second son of sorts. What was Mustafa's class? Berserker. It's not unlikely that Henry wanted to honor one of the people who treated him well in the Plegian military.
His other class option is Thief, which incidentally makes his class set the same as Gangrel's. Given that Henry used to be one his soldiers, it's unlikely to be a coincidence.
Why does the Wyvern Rider Cherche have the Troubadour and Cleric lines? She was originally training to be a cleric before she met Minerva. And she tamed minerva via, among other things, repeteadly whacking her with her staff.
Lon'qu is able to reclass as a Thief or a Wyvern Rider, the latter of which is pretty odd. However, he's originally from the western continent of Valm, where wyverns are much more common and raised for battle. The Thief line makes even more sense when you learned he grew up in the slums of Chon'sin.
Every character from Valm can reclass into Wyvern Rider: Virion, Cherche, Say'ri, Walhart and Yen'fay. Lon'qu also can, being one of only two pieces of evidence he might be from Chon'sin originally. The other is the apostrophes in his name and the name of his childhood friend Ke'ri.
Japanese does not have apostrophes, so this doesn't count. There's no evidence it's more than a choice by the localizing team.
One of Gregor's reclassing options is a Barbarian. In one of his supports, Lon'qu mentions that he once competed with Basilio for the title of West-Khan, but he was no match. Perhaps he learned something losing to a Warrior like Basilio and wants become as strong as him.
Olivia tells Lon'qu in their support that Basilio (who is like a father to her) talks often about him. In her efforts to be more useful to Basilio apart from being a dancer, having the option to reclass into a Myrmidon like Lon'qu seems like a good way to do it. Her growth rates are even similar to his!
This also makes it rather appropriate how Olivia uses swords even as a Dancer.
With how unnoticeable Kellam is, the Thief line being available to him is hilariously appropriate. He reveals that he was the most selfish among his siblings growing up, which also makes it fitting. Going unnoticed seems a weird trait for a knight, a class that is designed to stand in the way and draw fire from squishier units. But his reclassing options are Thief, a class renowned for their ability to sneak around (and, as an Assassin, gains the skill Pass at Lv. 15 which allows you to run right past enemy units) and Priest, a healer class which cannot attack and cannot take much punishment, whose top priority aside of healing is avoiding enemy attacks...
Ricken looks up to Chrom and sees him as a brother. His reclass options, as strange as they are for a Mage, are the Archer and Cavalier lines...which are the same as Chrom's.
Similarly, Sumia and Cordelia are childhood friends despite their opposite personalities. This is also reflected in their reclass options: the kind and gentle Sumia can be made a Priest (healer) or a Knight (strongly defensive unit), while the straightforward Cordelia can become a Dark Mage (offensive magic) or a Mercenary (balanced swordsman/woman).
Also of note with Cordelia's reclass options is the fact that she can use every weapon type in the game. She gets lances as a Pegasus Knight, Swords as a Mercenary, and tomes (including dark tomes) as a sorcerer. after promoting she rounds out with axes (Hero), bows (Bow Knight) and staves (Falcoknight). pretty fitting that someone hailed as a genius can use every weapon in the game (that's not class-locked).
Donnel's reclassing options are the fighter and mercenary classes, both of which allow him to become a hero. Pretty fitting for an underdog with fast stats growth. Donnel is your typical anime protagonist, going from zero to hero.
Nowi's reclassing is the same as Tiki's (Mage and Wyvern Rider), expliciting the former being the latter's Junior Counterpart. Plus, reclassing either Nowi or Tiki as a Wyvern Rider lets you have a dragon... who is riding another dragon.
Speaking of people who can reclass into Wyvern Riders: both Frederick and Sully have access to that class, despite neither of them having a connection to Valm (unlike Lon'qu, Virion, Say'ri, Cherche, Yen'fay and Walhart), any affinity for dragons (Nowi and Tiki are dragons themselves, and Panne can communicate with other animals), or any other flight-based classes (Aversa). I couldn't understand why those two even had that class...until I remembered that they both have supports with Virion, who is from the continent of Valm, with its large wyvern population. (And the Virion/Sully pairing is even fairly popular) It's a sort of Fridge Funny to imagine that Virion just up and decided to teach a couple of his friends how to ride dragons one fine day.
Tharja mentions in her S support with Frederick that Dark Mages require a certain level of mental instability in order to be good at their craft. Who are the specific people that can reclass to Dark Mage? All Plegians (including Noire), Miriel, Laurent, Libra, and your character. This may explain why characters like Ricken and Emmeryn cannot reclass to Dark Mage despite their impressive magic stats.
Gangrel cannot reclass to Wyvern Rider (a class common among Plegians) because he is afraid of heights.
Apologies for anything already mentioned. I just copy and pasted this.