Tifa's father hates Cloud because Cloud forced Tifa to go to the mountains, and then allowed her to fall. However, we the players, know better; Tifa and some friends decided to go to the mountins, because Tifa wanted to know what had happened to her mother (she died obviously - did her father not explain it propperly thinking she was "too young" or something? They never say...). Tifa moves further and further, towards the mountain, and one by one, her friends chicken out, but Cloud, who of course wasn't even "part of the group" (he was just passing) sees Tifa, and follows her - presumably to try and stop her from going to far. The game doesn't show it (because Cloud doesn't remember it), but Tifa falls, and Cloud also falls trying to save her or something. Her father arrives, and assumes Cloud is to blame - Tifa doesn't say anything because she's in a coma (Cloud has minor injuries).
However, what about when she woke up? Could she have, you know? Said something along the lines of "Oh by the way dad, that time at the mountains was my idea - Cloud was just there, he didn't force me to go, I didn't even know he'd be there." He obviously still blames Cloud because he is hostile towards him when he comes back in the 5 Years Ago scene. Why didn't she say something?!