Your analogy doesn't work; YC is buying equity just like anyone else. They're getting it cheap because they're paying for a couple undergrads to work for the summer -- your analogy would work if the bank would only give the loan if you had an established business and promised to work full-time for years.
Since we have the math, there's no reason to make up emotionally charged analogies. YC values these companies at somewhere between $100K ($10K for 10%) and $1.5 million ($15K for 1%). They do some legal work, and offer lots of advice and connections. Obviously, this isn't a good deal for everyone (given the industry I'm in, for example, I'd probably pass on YC), but if you're having trouble understanding why anyone would accept it, you may just have trouble thinking like a smart, ambitious, well-informed twenty-something.
And judging by the quality of your writing, age is not what sets you apart.