This is because mtr needs to open raw sockets, which it can only do as root:
$ mtr 8.8.8.8
mtr: unable to get raw sockets.
$ sudo mtr 8.8.8.8
Keys: Help Display mode Restart statistics Order of fields quit
Packets Pings
Host Loss% Snt Last Avg Best Wrst StDev
1. 216.239.48.53 0.0% 69 24.9 32.0 24.8 88.8 12.5
64.233.174.55
209.85.246.205
2. ???
3. google-public-dns-a.google.com 0.0% 69 24.9 26.5 24.9 35.9 1.6
This can be avoided by changing the ownership of mtr to root and activating the suid bit:
$ sudo chown root:wheel /usr/local/Cellar/mtr/0.85/sbin/mtr
$ sudo chmod u+s /usr/local/Cellar/mtr/0.85/sbin/mtr
You are probably reading this because you overlooked the "Caveats" in the install messages:
mtr requires superuser privileges. You can either run the program
via `sudo`, or change its ownership to root and set the setuid bit:
sudo chown root:wheel /usr/local/Cellar/mtr/0.85/sbin/mtr
sudo chmod u+s /usr/local/Cellar/mtr/0.85/sbin/mtr
In any case, you should be certain that you trust the software you
are executing with elevated privileges.