One thing that separates writing apart from many other fields is how easy it is for non-professionals to determine when it's done well. In fact, the definition of good writing basically is whether or not it has the intended impact on its audience.

If you are moved, the writing is good.

This is in contrast with other fields where "goodness" also requires other longer-term less tangible goals that are invisible to non-professionals. If a program does what you want right now, it may still not be made of good code because it can be hard to maintain, or fail catastrophically in edge cases or otherwise lack in ways that aren't immediately obvious.

You can be a poor chef who makes tasty food if your personality causes high staff turnover or your ingredient choices and pricing kill your profitability, all of which is hidden from the diner.

But the point of writing is to get an idea lodged in someone's head as effectively as possible, and we're pretty good at evaluating whether that's happened. The only case where it can clearly break down is journalism where the ideas you transmit must be factual in ways that require external validation. A compelling news story that is false may be good "writing" at some level, but isn't good journalism.

I see, thanks for the clarification. I agree that coding has long-term intangible goals that are difficult for a non-professional for to evaluate, and it makes sense that this isn’t something that people face in many writing-focused professions.

How do you evaluate and improve your own writing? Is this something that requires simply seeing the reactions of other people, or is it something you are able to simulate in your head? I think the reason why I thought it would be hard for other people to evaluate writing skills, is that I find it hard to tell when my own explanations are easy for other people to understand.

We usually point out examples of work done for clients in the same space. As for quality, the standards for paid work are unbelievably low in my opinion. My most recent real job was as an executive for a company that kept ghostwriting posts they intended to publish under my name. I found the content cringeworthy and couldn't even edit it to usable form. "Thanks for the effort but I would never use '...and stuff' in a post with my name on it.

The marketing team didnt understand my objection not because they were stupid but because the standard had been acceptably low for some time.

"How do you prove to others?"

The point of writing is to express an idea. You prove this to others by providing relevant metaphors (with respect to the subject, and to the intended audience), supporting ideas or evidence, and tie everything together into a concise, organized format.

"How do you tell if your writing is good quality?"

People listen. People take your opinion seriously. People respect you, and mimic your ideas or style of writing. The evaluation of writing quality is almost always a subconscious process, since analyzing communication itself is somewhat meta.

"it's really easy to evaluate technical skills like coding"

It's easy to evaluate coding, in some sense, because it's easy to communicate to a computer. Humans are much better than computers at thinking, communicating, evaluating, and responding to their input. So no, evaluating writing is more difficult and more subjective than evaluating coding ability.