Whereas, you could "write" programs by arranging little pieces of would with symbols on them on a board. You could punch hole cards for a mechanical loom, or you could solder electronic components together. None of that involves communicating with other people.
I think a better analogy than language would be a mathematical calculus - i.e. the way you can write down certain symbols, and manipulate them using certain rules, and you have certain guarantees about the result.
Another analogy would be a "kit" of standardized/conventional elements for construction, e.g. I-beams, windows, tiles, 2x4s, doors, cable channels, ... . You arrange these things, and if you do it properly, you get something meaningful and useful like a house.