FE6 was my first Fire Emblem game. I started to look for other franchises during the GC-GBA era. At that time, Super Mario was starting to rub me the wrong way with both Mario Sunshine and having Peach in Melee. The main Donkey Kong games pretty much died out after the N64 era. There wasn't anything new from Pokémon back then and when RSE finally came, that also rubbed me the wrong way. I also didn't have as much interest in Zelda, nor the other games. (*1)
The Fire Emblem came up from Melee, with Roy as a playable character. After reading stuff from Japan's Nintendo Dream magazine, there was also Lilina - who was another heroine not relying on the distressed damsel. (*2) I decided to try the game. GC and GBA games generally gave me the most disappointment/hate, but FE6 and FE8 (and for the matter Golden Sun 1 and Mother 1+2) were exceptions and were awesome games.
(*1) Zelda in Melee also initially rubbed me the wrong way. It was much later when I found out that Ocarina of Time started to downplay Zelda's distressed damsel role. After Twilight Princess actually made the dd role work and gave Zelda flaming!-Light-Arrows, all my hate for Zelda in SSB went out of the window.
(*2) At that time, of main females that didn't rely on the distressed damsel role, I only knew Misty and Kris from the Pokémon franchise. I only found out about Caeda around the same time as I found out about Binding Blade. Samus never interested me for some reason. I only played Mother 1+2, and found out about Paula/Ana much later on, after playing FE8.