Basically Apollo pissed Eros off. Eros, for pay back, used the arrow of love on Apollo and the arrow of hatred on Daphne(the arrow of love makes you fall deeply in love with the first person you see, meanwhile the arrow of hatred makes you literally disgusted by that person). Apollo saw Daphne, fell for her, but she screamed and Dan away from him. She reached the river where her father, the river god Peneus lived, and screamed for her. Her father transformed Daphne into the laurel tree to save her and Apollo still loved her so much to the point he made her immortal(evergreen) and so he's heavily associated with that tree.
This is the heavily shortened version, I couldn't find if Apollo and Daphne had any prior meetings. But I'm going to say that the discussion between Apollo and Eros is pretty accurate, just Daphne wasn't so layed off to let Apollo get his hands on her like the manhwa is making it look. Also that's why Daphne(in the manhwa) had that dream of tree branches wrapping around her.
omg thanks. I havent read this one yet cos from the one random chapter i read to test the waters (ch 14) the goldie seemed like an ass who is only chasing her now cos she liked him before and then tired of being ignored and tried to move on kinda trope… which seems kinda basic for the usually unhinged greek myths
Yeah, I get why you would feel like that. They didn't directly showed when they got hit by the arrows, it's just off screen and all. For people that aren't familiar with the original myth it can be confusing and/or get the wrong vibe. I'm a big Greek myth fan so I'm not surprised, it's just hard to imagine an ending when this "love story" is supposed to be a tragedy. The only complain I have is how the arrow of hate isn't shown "accurately" but can't do much about it. I'm just glad that it's not another "Persephone and Hades" retelling XD

like did they fall in love with each other? or one way love, other way good fuck? or is it one fall bam something happened the other fall oh no too late kinda stuff? cos i hate one way yearning