You’re right that not all causes are reasons. In fact, I think causes and reasons are different things in many cases. That’s kind of what my examination of forward-looking and backward-looking reasons was about.
To take it from a different semantic angle:
You’re right that I didn’t arrange for the tire to go flat. That would have been me providing the physical cause, or backwards-looking reason. But what I did do, was provide the forward-looking reason — as in the “what could the reason for this happening possibly be?”
If that is the question of a forward-looking reason, what I’m arguing is that we answer it. Furthermore, we can provide that answer with our mindset and actions long after the initial event took place.
That may benefit from more unpacking if we further this discussion, but I think that’s a better way of saying what the rest of the article was hinting at.