If you give a founder (or early employee) more than they're going to be worth in the long term, you'll feel increasingly motivated to fire them and recover their un-vested stock. If you give them too little, they become increasingly motivated to quit and start something they can own.
From what you described, you were at a lose-lose impasse. One or other of you was going to end up unhappy, in a company-destroying sort of way. I would have quit also and would make sure to sort the ownership question out earlier next time.
Somewhat tangentially, people also tend to over-value the ownership that their "idea" should entitle them to. If someone spends 3 months thinking day and night and you just started, it can seem like they deserve a big chunk. But you have to remember, standard vesting is 4 years, so their 3 months of thought is only about 6% of the time you're each committing to the business.