Why Choose Gentoo:

Gentoo is fairly fast.   But it is promoted only partly for speed (see here and here).

Gentoo supports a variety of architectures:   Alpha, AMD64, ARM, HPPA, IS64, PPC, Sparc, x86, and more.

-- As a comparison, the well-funded Ubuntu distro officially supports only these three:  x86, AMD64, and ARM.

Gentoo's unique package management software  ("emerge" and "portage")

       --  One user-editable text file keeps a simple list of all installed software (not including dependencies, which are managed automatically).  This makes it easy to see what you have installed, choose packages to uninstall, etc.

       --  Customization of individual software packages (via USE flags)

       --  Multiple versions of packages are available, so that you can often install an older or beta version in addition to the current stable version.  If the older version is no longer in Portage, then you can still download the ebuild from the Gentoo CVS repository.

       --  Easy to create your own "package"   -- or edit someone else's and install it.

                         --  And thus, compiled-from-source software is actually recognized by the package manager  (usually not an option for other distro's).

       --  Cutting-edge packages & kernels.   It doesn't take much as much work for new releases to make it into Gentoo, since Gentoo package maintainers only need to update a text file  ("ebuild")  with any new instructions for compiling/installing, rather than the traditional method of updating the package maintainer's build/install procedure, then doing the compilation, then posting the resultingbinary package.    The Gentoo "newness" factor is great for getting bugfixes and the latest new features.

       --  Ability to pick-and-choose individual programs.  For example, if you run Gnome or XFCE and just want to install Konqueror (from KDE), you don't have install all of KDE.

       --  Programs, when you install them, don't automatically add themselves to the list of apps that are auto-run at boot time.

       --  Ability to install & run multiple versions of some programs simultaneously  ("slotting").

       --  Upgrading software packages doesn't overwrite prior configuration files ( stuff in /etc/ ).

                        --  Easy interface for choosing to keep the old configuration, use the new one, or merge the two.

                        --  Even provides a revision control system to keep a log of the past content in each configuration file  (dispatch-conf & RCS).

Kernel

          --  Forces you to be in a position where you are ready to edit your kernel configuration and recompile/reinstall it whenever needed.

Rolling upgrades
          --  Meaning that you don't have to cross your fingers, wondering if upgrading the entire distribution at once (a.k.a.  "dist-upgrade") will break something.

          --  Also meaning that you aren't locked into a certain range of software versions for your particular version of the distribution.

Purity and Integrity of Software

           -- Software is installed (mostly) straight from the source code on the upstream author's website (or an exact copy of it on a Gentoo mirror), and not with customizations by a middle-man (your distro), which are usually non-apparent to the user.

           --  But if any patches are part of the normal Gentoo install, you can look at this beforehand, you will be notified of it during the installation, and you can prevent the patches from being applied  (by commenting out the appropriate lines in the ebuild).

Installation of OS has lots of options & flexibility (some distro's don't offer LVM during install, etc.).

            --  And the "minimal install" ISO is very small.

Custom System Parameters:

            --  "Gentoo makes it very easy to have machine "profiles" which mandate software versions, optional features (USE flags), compile options and even base packages which must/must not be installed. So for example I have a web server template which requires a modern gcc to be used, hardened compiler flags to be used, certain versions of nginx to be installed, again with various default modules that nginx should support. So in many ways something like Kickstart for Redhat... But the cool thing is I can update the template right now and then all my machines pull in the changes and rebuild whatever is required to get to the end result!"   (from here)

Experience:

            -- Decent documentation & community help

            -- Good learning experience for how a Linux system works