In an industry that has popped up only in the last 30 years, has changed rapidly and reinvented itself every 5 years, it's hard not to feel like an impostor sometimes. A lot of what we're doing is new, we're first-generation web developers, none of us have 15 years of experience with React, or 20 years of experience with HTML5 because those things didn't even exist then!
Often when you're feeling like this it's because you are unaware of your own worth. I'll explain the moment when I snapped out of feeling it myself:
my background: I've been building websites since ~2000, went to school for Graphic Design (where we were taught frontend web development a little) so I have both a long history, and formal training for the type of work I do. Yet since I have no Computer Science background and didn't learn programming, sometimes when I'm working alongside programmers and other non-designer web developers I feel like an imitation, or like they'll think I'm stupid for not knowing something 'basic' to them.
Well, I helped out with Ladies Learning Code, and I wasn't the instructor - just a helper. But what I saw was that there were people there who were competent, educated adults who had never done web design before, and after 1 session of HTML/CSS they felt confident telling others that they were now 'web developers'.
I also met people who had gone through 3-week 'bootcamp' and pivoted from a totally different field, and had just been hired into their first web development job. They went from nothing -> pro in 3 weeks.
So what was I doing doubting myself after 15 years? Surely I was in the same position they were in skill-wise before I entered high school, but here I was struggling with impostor syndrome after school, college, and working in the field professionally.
After that day, I no longer feel bad telling people I'm a professional web developer, or worrying or wondering how I fit in compared to my peers. There are people today who might have never touched HTML before who will apply for jobs later (after their workshop) claiming they know the tech and are pro web developers. You can too!