The bike profile in OSM routers will prioritize bike paths, bike lanes, and small streets over big highways, but there's always a balance since you're unlikely to want to bike 10 miles out of your way to avoid a busy street. That balance is always in flux and can only ever be as good as the OSM data underlying it (road classification and bike tagging etc)

If you bookmark streets that it's sending you down or avoiding inaccurately and check them out later on a computer, I bet you'll find that there's some OSM tagging issue. https://osm.org has a routing tool you can compare with as well. The OM Telegram channel is always willing to take reports on where OM routes are worse than OSM.org routes, and OSM channels are happy to help figure out what tagging issues there may be.

Cheers!