You will eventually come to learn that your time is precious, and that wasting it on an idea that can't be made to work is worse than failing to make one (of many possible) viable ideas succeed.
For some context, my product is a loyalty program for bars and restaurants based on Facebook's check-in. I talked with 50+ restaurant owners, and social proof is very important. But i also learned that no restaurant is totally satisfied with my competitors' products. I learned where I need to perform (final customer's adoption, as it is a B2B2C product). And I am testing my premises on these 5 clients. These next two months will be crucials to validate my business. I actually put a hold on sales to take good care of these clients. If in two months there are willing to pay for it and let me put their logo and cases on my marketing material, then I have a business. If not, then it is time to quit (or pivot). Either way, I still need a month or two, at least, to know if it is a good idea (or if I am good enough executing it). So I am taking this angel money to validate a promising idea. Sound exactly what angel investment is designed for.
In your position, I would pick a different business idea.
Yeah.. I'd say take the funding.
I still prefer the angel investment.
I could make a house building analogy here probably.
I started to sell my product from month 1, but wasn't able to generate revenue from month 1. I have a SaaS for restaurants, the sales cycle is longer than a month, no restaurant (around here) close deals at the end of the year - this I learned from experience, but also from successfull and experienced entrepreneurs from the same market; also advised by these successful founders I am offering a 3-month free trial for the first clients. The advice actually was "you will only charge after the 10th client, you need social proof first of all, so give your product for free and then charge after the 10th early-adopter."
So, there is no way I can be profitable before March or April. Ok, maybe I am no sales wizard, maybe I am not good enough on this founder thing. But the point for me is, I am broke, and I already started my company, and I can't make it profitable. As I can't choose option 3 "go back in time and found another business" and I am not ready to quit this business, I will take funding.