Unlike Homebrew, APT manages the entire system - from bootloader to browser. It is designed to work in multi-user environments where you don't want 40 different users installing 40 different copies of the same program, not updating them, getting viruses from unpatched software, and ruining the well behaving user's day.
Instead, software is installed once under root privelages so regular users can't sabotage each other, and everyone can share the same up-to-date copy.
It is possible to compile and install software per-user (without root) as well, and by setting $PATH you can have your user-installed software mask the version installed on the system. I recommend doing this for software which cannot be obtained through the package manager, or for bleeding edge git HEAD versions of stuff. Otherwise, let the knowledgeable maintainers of your distribution do the work for you.
Instead, software is installed once under root privelages so regular users can't sabotage each other, and everyone can share the same up-to-date copy.
It is possible to compile and install software per-user (without root) as well, and by setting $PATH you can have your user-installed software mask the version installed on the system. I recommend doing this for software which cannot be obtained through the package manager, or for bleeding edge git HEAD versions of stuff. Otherwise, let the knowledgeable maintainers of your distribution do the work for you.