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I'm ignorant in this kind of tradition could someone explain it to me? Where I come from when a blade would serve for decoration or simply (depending on whether or not the person who gave it knows how to maneuver it) a sign that he will teach you to use it in defense. It also signals that he/she trusts you to know how to defend himself or even defend him/her if the need arises.

Human Traditions
Barbatos, unknowing of human mores, gave you a heartbreaking gift without knowing. Satan helps him patch it up♡
fluff; gn!reader

Barbatos' gaze lingers on you throughout the lesson, barely focusing on the teacher's words. Satan notices the butler's longing eyes, scooting closer to him.
"Trouble in paradise?"
Barbatos glances at the younger demon, needing a moment to remember what that phrase meant.
"Mc hasn't been talking to me."
"Hm? I thought things were going so well?" Satan continues, obviously glad to have found a new distraction from the boring lesson.
"I must have misunderstood," Barbatos responds flatly, seemingly accepting his fate and broken heart.
Satan furrows his brows, feeling his detective senses tingling. There must be a reason for your behavior, particularly because he remembers the hearts in your eyes whenever you and Asmodeus gushed over your crushes. From the beginning on, yours was always Barbatos.
He starts questioning the butler, asking for the details of their latest interactions.
"... and the gift was the last thing I gave them before they started ignoring me," Barbatos finishes his summary of your whole time dating while walking to lunch with Satan.
The fourth born closely listens as he tries to fit the puzzle pieces together in his mind.
"What kind of gift did you give mc?" he asks, feeling like there's only a small fragment left before it all makes sense.
"A very fine blade, colored in mc's favorite hue. I thought they'd appreciate the meaning it holds."
Satan stops dead in his tracks, finally having found the underlying problem. He shakes his head while laying his hand over Barb's shoulder, quickly explaining the meaning of gifting sharp objects to humans.
Barbatos pauses for a long second, his eyes filling with subtle horror.
"I see..."
Satan immidiately offers his help, which Barbatos gladly accepts, feeling insecure about his knowledge of human customs now. Satan starts working on a plan as soon as he arrives home, researching human traditions and mores and documenting everything he can.
Barbatos is happy to receive his notes the next day, studying them thoroughly and making a plan to win you back and clear up the misunderstanding.
The demon is confident in the letter he wrote and the white moonshine tulips, which he places on your doorstep, slight nervousness haunting him as he leaves the HOL unseen, hoping to have you back in his arms as soon as possible.