I feel this way sometimes too, despite having a traditional CS degree and being in the software industry my entire professional life. Apparently impostor syndrome is more common than we think.
Personally I've come to believe there are very few people who "fit like a glove", and everyone else has varying degrees of this.
Edit: On rereading this it might appear that I am trying to diminish/dismiss your experiences. I apologize if it came across that way - my intention was more to share that I've heard this same sentiment for different reasons from many different people.