I am trying to learn arch and thought it would be useful to figure out how to edit or compile packages.

It always bothered me that on a clean install with just about any graphical component you'd always get "Avahi Zeroconf Browser" as well as ssh and vnc server browsers.
So I thought it would be great to make libcups without these avahi components.

Unfortunately, I don't quite understand how to achieve this. I tried getting libcups-git from AUR and editing PKGBUILD file. Setting "--enable-avahi=no" flag didn't seem to get rid of the browser and other stuff.

Are there more flags that aren't in the file itself? Or I am supposed to edit something else?

Did you even uninstall the original package, and install the git package?

I suggest you look at the source files for the libcups package first, most notably the PKGBUILD. Compare that to the AUR git package and its PKGBUILD.

Are you familiar with the ArchLinux Package Creation process?
There's a lot to read for you.

Then show us what you did and where and how it failed.