> Nowadays, I read everything I write out loud and if it sounds awkward (or not like me) then I just delete it and write it again from scratch. Oftentimes it helps to just close my eyes, say what I want to out loud, then write down what I just said.
This does sound like editing to me (in a good way). Unless you meant something else when you wrote that school taught you to focus overtly on the editing stage.
Now that you mention it, my old style of editing might have been something that I learned, rather than was explicitly taught.
I used to frame writing as a painful activity, so once I had a "workable" rough draft, I would break out a scalpel and try to make it readable with word surgery. I would spend hours staring at the same few paragraphs, and it was horrible.
Now I just delete it. It feels like a clean slate, but the slate in my brain has made opinions about what's important to say and how to say it better.
The two approaches exercise completely different muscles, and what I like about the "rewrite" approach is that it exercises some of the same muscles that will help me communicate myself properly on the first try.
This does sound like editing to me (in a good way). Unless you meant something else when you wrote that school taught you to focus overtly on the editing stage.