Why would anyone want to compile all of their software? I'm sure it has some advantages, but I see a few disadvantages. Compiling KDE can take days. I know that portage can be customized by telling it what flags to use when compiling. What are the other advantages to compiling software rather than downloading and installing binaries?

the biggest advantage would be you could compile the source and modify it to your needs. or use the source with some extra commands like I had a program to install which installed smtp support, so that it could mail reports, I didnt want it that to compile. I inputted --no-smtp-support or something and I didnt need to install/configure a smtp server for it. whereas in the binary you would have to install it.

well the best example would be of the kernel. you edit it to your own requirements and compile it. you wont get that compatibility with bins.

The USE flags are the major advantage of Gentoo but if you don't like building everything from source then just use another distro. If portage really turns you on that much then install FreeBSD and use Ports, the original. You can install stuff from Ports (which is from source) if you like or you can use pkg_add -r to install from binary. Gentoo has binaries available too but last time I used it they didn't have bin versions of many packages.

If I were going to use Gentoo, I wouldn't want binaries. I think that having software compiled on my own computer would run better than software compiled on another computer. I had Gentoo, but my laptop quit working when I was installing KDE.