Opening the book…
The saw doesn't know your hand from a scrap of pine. A blade at speed will grab and pull faster than you can flinch, and the shortest path for your fingers is straight into the teeth. Most serious shop injuries I've heard about start the same way: somebody reaching across a tool that was still coasting down. The offcut you're grabbing isn't worth what it can cost you. Wait, and then reach.
Kill the power and keep both hands planted until the blade stops turning completely, not almost. Clear offcuts with a push stick or a scrap of wood, never your bare fingers. Set up your workflow so cutoffs fall away to the side on their own instead of piling near the teeth. If you catch yourself reaching, freeze on the spot, and build a firm habit of stepping fully back from the tool before you gather up any parts.
There's no version of this where reaching over a live blade is fine. The only bend is the direction you approach a stopped tool from, and even then you keep your body clear of the blade's line in case of a surprise restart or a bumped switch.