I actually have a Love/Hate Relationship with the Fire Emblem Franchise. So here are the things I really don't like in Fire Emblem which is pretty much most of them ,
Weapon Durability: Granted this is a Strategy Game where you're supposed to manage every single thing to raise your odds of winning, but still it drags the game down to a crawl having to ration your weapons. FE4: Geneology kinda fixes this issue, but Gaiden was smart enough to remove this staple feature since it's such an archaic game design choice that makes most of the Fire Emblem games be not about a Strategy Game based on Fighting Battles, but more so on Strategy based on Weapon Management. Plus, it makes using most of the Legendary Weapons in Fire Emblem Games pretty much pointless to use except for beating the Final Boss with it.
Promotion Items: I would've like it if it would be possible to promote in the Preparations Screen for the next battles instead of using a specific item to promote your characters, but oh well. It's the least of my worries.
Character Growth Rates: I really find this to be pretty underwhelming as the growth rates of *insert attribute here* I see in most of the Fire Emblem characters range from average to straight up bad (Even the Est archetypes don't amaze me despite their high growths). Getting RNG-screwed is the norm in most FE games so I would've liked this staple feature be utilized to its true potential since I don't think it is due to it being inconsistent. Generally I prefer characters with great bases over great growths like an Ogma, Oifaye, and Seth like characters where they stay good to the bitter end since they have OK growths. Other strategy games like the Shining Force series did a decent job managing consistent growth rates for your characters.
Bear in mind, I still like a lot of things in the Fire Emblem Franchise. Mainly the storytelling, the characters, the world-building, and the fact that this is the grand-daddy of Console Strategy RPGs that started it all.