Couldn't open a raw socket. Error: Permission denied (13)

Solution 1:

Did you install nmap using:
$ sudo snap install nmap
or
$ sudo apt install nmap
I had this same issue, I installed using snap and was getting the same error as you. If that is the case remove the snap install and use apt:
$ sudo snap remove nmap
$ sudo apt install nmap
run a command with nmap, if you get the error:
bash: /snap/bin/nmap: No such file or directory
use the following command to let go of the cached link:
hash -r
run nmap again,this worked for me.

How I got my answer.

Solution 2:

You have to grant network access to nmap with: snap connect nmap:network-control