As it has been pointed out below, this is a cleaner way of doing it, instead of getting around the Security features of OS X.
sudo gem install -n /usr/local/bin cocoapods
I'm assuming you're running OS X 10.11.
This is happening because Apple has enabled rootless on the new install.
If you type:
sudo nvram boot-args="rootless=0"; sudo reboot
in terminal.app, your computer will reboot with it disabled.
Once that is done, type:
sudo gem install cocoapods -V
the -V is for verbose and will spit out any errors if they happen.