“The bitter end” did not originally mean a painful or miserable finish. It began as a nautical term. On a ship, the bitter end was the end of the anchor cable or rope that was made fast to the bitts, which were sturdy posts on deck used for securing lines.
In other words, the phrase referred to a very specific physical end of a rope. If the anchor line ran out all the way, you had reached the bitter end. That concrete meaning came first.
Later, English speakers connected the phrase with the ordinary adjective bitter, meaning harsh or painful. That helped the expression develop its modern figurative sense: continuing through something difficult until the very end.
- Original nautical use: the rope reached the bitter end.
- Modern figurative use: they fought the lawsuit to the bitter end.
So the phrase is a good example of how a technical term can become an everyday expression, especially when the words already suggest a broader meaning to later speakers.