Why does it seem like everyone thinks they can code, but very few people actually have the skills necessary to be successful as software engineers and programmers?

Because it looks easy, and the vast majority of humanity overindulges in narcism and wishful thinking.

Everybody also thinks they can write - but spelling, grammer, and a good vocabulary do not a writer make. That takes having something worth saying, and some skill in saying it well. Everybody thinks they can drive. Everybody thinks they’re great in bed.

With most things - it takes thought & hard work, just to get started - and it takes a lot to write a first draft, or build a prototype. With software, you can pound keys, move fast, break things, and fix them later - assuming nobody has died from the errors.