History & Etymology
Originally coming from the Proto-Indo-European kehd the word Hate actually took two different paths to find its way in to modern english. Kehd originally simply meant strong emotion, but from there the word followed two paths one leading the the noun form and the other to the verb.
In Old English the noun form of the word hate was hete and was later modified to conform with the verb form hatian before it become the word we use today.
The noun form hete has pretty much meant what we mean when we say the word hate today, and came from the Proto-Germanic hatis- which is also the source for many other european words for hate. Modern german hass, and Dutch haat.
But the verb form is where things get a little bit more interesting. Hatian goes back to the kehd- which meant sorrow. It’s also the origin of Welsh cas meaning pain or anger and greek kedos meaning sorrow. Following the rules discovered by Jacob Grimm the k sound at the beginning of kad- became h sound and it formed the word haton in Proto-Germanic meaning to hate in the same way we mean it today. From there it became hatian and eventually the word we use today.
It’s easy to imagine how a word meaning sorrow and pain could come to be conflated with the word for hatred. When something hurts you it’s completely natural to feel anger. Really isn’t that what hate is, a combination of anger, sorrow, and pain.