I go to cool app website, I click download, I get a '.deb' file, I click .deb file, it opens some installer GUI (instead of Ark because I'm lucky today), I click install, I get error, I google error, I find cryptic commands that modify my system in weird ways just to get the app to install, I install app, I open app, it crashes, I open firefox, I get error "error: libX.so.1.2 not found", I can no longer google the error.
The system package manager is convenient when it works, because it's already there. But that's about it. Using it to install any random apps is a recipe for disaster, it leads to fragmentation since everyone on a different distro uses different commands/workarounds to fuck up their systems in different ways when trying to install poorly packaged software.
If everyone just used Debian, we wouldn't need Flatpak, but obviously that's not the case. Whenever you find a "linux app" that's packaged for distroA, but you're on distroB, there's a chance that it will work. That is 100% luck and coincidence, because most linux distros just so happen to ship the same family of system software/libs, sometimes even with the same versions.
Rather than leave it up to the undefined behavior lottery, a standardized non-system packaging format can guarantee that things will work across any distro. That's better for everyone involved: users, sysadmins, distro maintainers, and developers. Whether Flatpak is that format idk, but IMO it's the best overall out of the three main contenders (Flatpak, Snap, AppImage)