Wouldn't make more sense for her to start out at the [Hate] level?
Ah, but the God of Conquest, Keima, says that hate is an important step towards love... in gal-games. It means they have started to think about you more than they did before. (Do not try this at home)
Very true. Plus it makes the jump to Normal much more satisfying.
Going from 0 to 1 [Normal -> Like] is nice, but going from -1 to 0 [Hate -> Normal] is much more impressive.
This is basically the reason the concept of "tsundere" exists. (No really, science has been done to prove tsundereness works!) We are, as social creatures, designed to pick up on it when there's a change in how a person reacts to us, so if someone starts out hostile and then mellows out, we perceive it as forward progress, and react more favorably to it in order to encourage more of that change than we do to someone who starts out nice staying nice. (And people tend to react coldly to the always-nice ones, asking if there's something they're hiding, while someone who started out hostile then became a little less hostile is regarded more favorably.)
Beyond that, "the opposite of love is not hate, but indifference." It's easier to turn someone who hates you into someone who loves you than it is to make someone who doesn't notice you exist care about you in the first place. (Although the expression more often refers to how people can ignore atrocities committed out of sight and out of mind that they would never do to their worst enemies, it does apply to this sort of situation as well.) For the same reason as above, if someone is combative towards you, and you actively try to repair that relationship, then unless they're dead-set on hating you, then they'll react positively to those attempts.