Eagle Autorouter will not route my board.

but for the through-hole components based PCBs, I would strongly like to recommend to try the auto-router.

Well the issue is that it doesn't take things like priority signals into account or the requirements of ground planes in certain places etc etc.

If you're doing starting out and learning then it can be great but otherwise I'd probably stick to manual routing (or at least manually route some of the tracks first)