One example of this is what I will generically call the "Google Interview". I know brilliant engineers how have done massive non-trivial projects that have generated millions of dollars in revenue who could not pass such an interview.
The other aspect is the constant exposure to the language-of-the-day and framework-of-the-day club. I can see a young aspiring developer becoming utterly disappointed when realizing it is nearly impossible to keep up with it all. Where do you start? How do you learn this stuff? Someone could very easily think they are not up to par if they can't walk in these mythical shoes.
The truth is very different from that. There's a huge world out there for software engineers. There are real problems to be solved. And, no, not everything in software engineering lives and dies on a web browser or a smart phone.
Is the OP saying that she needed to feel like a hacker to feel legitimate? That would be sad.
What the hell is a hacker anyway? Definitions abound. In many ways it is more about how someone might approach hardware and software problems than anything else. You don't have to be YC material to be a legitimate software engineer. One could very easily argue there are tons of software engineers out there doing far more important work than almost any YC developer has done to date. Most of them are invisible. Think about the people writing code for MRI machines, aircraft avionics or even your car's ABS system.
If you are young and love software engineering please don't think that building websites is the only way you are going to become somebody in this business. Explore what's out there and dare to learn about other interesting problems you might be able to solve.