brew install python3
Warning: python3 3.6.3 is already installed, it's just not linked.
You can use `brew link python3` to link this version.
brew link python3
Linking /usr/local/Cellar/python3/3.6.3... Error: Permission denied @ dir_s_mkdir /usr/local/Frameworks

发现 /usr/local/ 下没有路径 /usr/local/Frameworks,需要新建该路径,并修改权限。

解决思路

sudo mkdir /usr/local/Frameworks
sudo chown $(whoami):admin /usr/local/Frameworks

成功:

$ brew link python3
Linking /usr/local/Cellar/python3/3.6.3... 1 symlinks created