[WJW]

AFAIK learning to program these days is a fairly normalized process where people start with basic commands (ie hello world stuff), then move on to control flow (if/while/for) and eventually on to object oriented programming, higher order functions and all the rest. Some people even go on to do things like "craft your own interpreter" and "NAND to Tetris" to really round out their knowledge, but most do not and that's fine. I think that some of the simplest programs are just as "explainable" as your washing machine example. Conversely, there are plenty of machines complex enough that an average person has no idea how they work. A MRI machine for instance is just a collection of metals and hoses and most people would seriously struggle to point out which parts do what and why. It's still not magic though.

I guess the difference between magic and science to me is that "not everyone can learn magic", but the core bit that makes science work is that in principle everyone can learn it. In practice of course we cannot know everything and so have to rely on the expertise of others, but that is a limitation in the humans and not in the knowledge. Meanwhile for "magic" you have to be chosen by the gods/genetically gifted/cursed/whatever.

In a universe where magic is just another skill that anyone can learn, that reasoning goes right out the window of course.

[AlotOfReading]

A lot of other magic systems are in principle open for anyone to learn. I mentioned this a bit more in the other comment, but buddhist spells are open to everyone in principle. The chosen/gifted one is a feature of western magic systems because of our own cultural expectations.