Error installing cocoapods "sudo gem install cocoapods" MacOs Catalina

I think you don't have the commande lines tool on Xcode...

sudo xcode-select --reset
xcode-select --install

Keep us posted...

Seems like you don't have access to usr/bin directory. i have been there!!

please try below command.

sudo gem install -n /usr/local/bin cocoapods

this should work. Thanks!!

Please refer this post more information about access rights.