I’m pretty sure there’s nothing that ever indicates he can read, and I def headcanon him as illiterate. Like, unless Griffith gave him lessons I don’t see where he would’ve learned.
On the other hand we’ve seen Casca reading and she didn’t have much more opportunity for formal education than Guts. And there’s no indication of where back alley peasant kid Griffith learned to read and write either. So who knows?
I need art of Guts trying his best
Griffith would have found some way to learn regardless, and I wanna say maybe Casca learned as part of wanting to be useful to Griffith? Even though “being his sword” directly implies combat, I can see Casca wanting to be good in any area she can manage.
Same could maybe be said for the Guts who wants to be Griffith’s equal, but imo before he set that as his goal he was mostly focused on his role as the raiders’ captain and I don’t think that, at that point, he was embarrassed that he can’t read and Griffith can. Maybe later but yeah.
It’s still possible that Griffith tried to teach him for fun but I can see Guts being like “this is stupid & impossible” and just giving up about as easily as I can see him trying in order to impress Griffith. So yk. All headcanons are valid here I feel.