GA encompasses a huge range of aircraft operations, some of which look a lot like airlines and some which don't. For instance, a student at a flight school is very different from a private jet. That said, most GA operations are VFR in small, low, slow planes.
While it varies by country, VFR aircraft are generally not required to file a flight plan nor, in most airspace, even talk to ATC. You can just get in your plane, take off, and for the most part, simply fly wherever you feel like, whether that is sightseeing around town or crossing the country.
Similarly, even if you do talk to ATC, it is a lot easier for ATC to keep planes separated if they're moving at 100kt rather than 500kt. So, they don't need much ability to predict where you're going because they have time to just watch and see.
Also, small aircraft have a much wider range of performance and mission profiles, from training to crop-dusting to pipeline patrol to cross-country flights spread across thousands of small airports, whereas jets are generally all trying to fly at the same optimal altitude for as long as possible between a handful of medium to large airports.
All of these factors combine to result in airline (and to a lesser extent charter jet) operations end up needing a lot more work to keep them from bumping into each other. Airways (and things like SIDs and STARs) help ATC manage that complexity.