I was 50/50 voting partners with a co-founder of my business. I am 22 years old and have never built a business but I came up with this incredible idea, wrote the original business plan, etc.
My reason for resignation was specifically because of the fact that I had been compelled (by way of my other cofounder threatening to leave if we didn't continue with his way) to make strategic decisions that (now that we weren't hitting major deadlines) were clearly not the right strategic decisions being made. And now that I want to resign for that reason, and we are trying to get it in writing that that is my reason for resignation, he is telling me that it cannot be my reason for resignation because he believes he will not get investors to be able to invest in the company (in order for the company to continue functioning) if my reason for resignation is a disagreement regarding the strategy that he threatened me to follow in the first place. So, should I be able to resign from a company for my own reasons for resignation?
You can quit from anything for any time for any reason. You, or other people reading who want to leave a similar arrangement, may have an operating agreement in place which describes what happens. You still have shares to deal with, for instance.
Next time, work out a way of dealing with people up front. That way, disputes will have a path to resolution instead of ending up in this emotional mess you're in.
The two of you sound like neither of you really understands business or how business ownership works. Is there value in this business? If there is, you should consider talking to an attorney to protect your rights and property.
Your co-founder's concern that nobody will fund the idea if you leave is less important than he believes. People make changes all the time. The question is: does the idea have life in it? If there's genuine value, your being there or not won't have much impact on funding decisions. Yes, founder credibility is important. But it's not the only thing, or the main thing.
You are way too wrapped up in this thing emotionally and my advice is that you find ways to disconnect yourself from it entirely (including ownership) ASAP.
The most important lesson you should learn from this experience is that trust is the basis for all relationships; business and personal alike.
You chose your partner because you trusted them. On some level you trusted them even though you do not explain how. Over the course of the relationship, you stopped trusting them and even feel threatened by them. That's not healthy no matter what the situation may be. You should leave. The question now becomes how do you leave.
Since this is a startup you have two hats/roles you can leave from: founder and worker. As a worker you provide your work contribution and can leave at any time as long as it is within the scope defined by the law. If there is no work contract then probably you can just stop working. As a founder it becomes a bit stickier because it depends on the legal structure the business is in: limited liability company, corporation, or something else. However, because the idea was yours and you wrote the business plan you may not want to give up your ownership interest in the business. That's fine too. You don't have to do that. You decide. If you do want to leave ownership behind then you sell it to your partner. Since they are convinced they will get funding I'm sure they will be happy to buy your interest.
No one can stop you from resigning. if they want you to resign for other reasons, they should pay you and reach a settlement agreement (which would cause you to resign for other reasons).