I highly recommend you both read this article on the subject: http://www.themacro.com/articles/2015/12/splitting-equity-am...
Perhaps that will help you reach an agreement or part ways if that isn't possible.
I can offer a relevant perspective because I pursued my startup solo. I have said for a while that if anyone asked my opinion my response would be, "don't do it." My understanding is that Y Combinator prefers teams as opposed to solo founders because of the amount of work and the truly gut-wrenching process of bringing anything to market. I agree.
I am fortunate because I am married. The strength of will not just to weather the storms, but to remain focused, positive and productive is a shared contribution with my wife and I. She has no interest in being considered a founder, but the value of her contribution in that regard, is indisputable.
Even with a great support system and a decade of experience in my field everything took longer. When there's a "million" things to do and nothing else gets done while you are doing something it's easy to lose heart. So, I would recommend valuing the partnership beyond your individual contributions (assuming it is effective/satisfying/pleasant - aside from the split discussion).
My personal opinion is that a quality partnership is worth 5-10% difference.
If the cofounder can give you a clear execution edge, then the said cofounder might deserve a higher share. Some examples include: 1) Existing business relationships with potential clients 2) Experience starting and selling startups (which gives you a big edge in raising capital) 3) Commanding expertise in the domain that you are in (i.e. start a video company with a hollywood producer) 4) Specialized technical knowledge (i.e. one of few PhDs in the world who knows how to build autonomous vehicles)
If it's very difficult to define the "execution edge"/value of someone then that person probably shouldn't be a founder, or the other founder(s) undervalue that person. In either case this should be a major red flag.
I fully agree that being the idea man is a bad reason for unequal splits. I'd also be more optimistic about the chances of resolving that issue vs the issues related to an undervalued/incompetent founder.
I won't partner up with an idea person anymore. I have found that they always feel entitled to more of the equity and I suspect it's because they are insecure about their own abilities (which usually ends up being something you can do yourself).
I will, however, partner with an idea person if they also offer a sizable investment into the company.
Your cofounder should be bringing something to the company. Either money, connections in the industry, or some other type of skill.
If you are both developers or one person has just the idea, you will run into issues at a later stage in the development of your company.