You can't remove glibc! If you do, all your programs will stop working (including pacman). There isn't a single Linux program other than the kernel that doesn't link to libc.
I'm no expert on Arch, but if you want to understand what libraries are, look at
this blog.
You might also consider trying a different distro. Arch is usually considered an expert's distro, and it is liable to mismatches between applications and libraries because it uses the latest "bleeding edge" versions of everything. I wouldn't recommend it as a first Linux for anyone. You might be a lot more comfortable with Mint or Ubuntu.