Hey there, let's work through this issue together—no sudo required, promise!

First: Fix the Brew Permission Issue #

The error you're hitting happens because your user account doesn't have the right permissions to create or access /usr/local/Frameworks. Here's how to fix it properly:

1. Create the Frameworks directory and set correct ownership
   Run these commands in your terminal (the sudo here is only for a one-time ownership fix, not running brew itself):

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

2. Relink or reinstall Python3
   Now try linking the formula again:

   brew link python3
   

   If that still fails, reinstall Python3 with brew:

   brew reinstall python3
   

3. Fix broader /usr/local permission issues (if needed)
   Sometimes other subdirectories in /usr/local might have incorrect ownership too. Fix those with:

   sudo chown -R $(whoami):admin /usr/local/bin /usr/local/lib /usr/local/sbin /usr/local/share /usr/local/etc
   

   This ensures your user owns all the directories brew needs to operate, preventing future permission headaches.

Alternative Ways to Install Python3 on Mac (No Brew Needed) #

If you'd rather skip brew entirely, here are reliable, hassle-free options:

• Official Python Installer
  Grab the installer for your desired Python version (3.6.5 in your case) directly from the Python official release page. It will automatically set up python3 and pip3 in your system path, and install Python to /Library/Frameworks/Python.framework/.

• pyenv (For Version Management)
  pyenv is ideal if you need to switch between multiple Python versions. Install it via git:

  git clone https://github.com/pyenv/pyenv.git ~/.pyenv
  

  Then add these lines to your shell config file (.zshrc for Zsh, .bash_profile for Bash):

  export PYENV_ROOT="$HOME/.pyenv"
  export PATH="$PYENV_ROOT/bin:$PATH"
  eval "$(pyenv init --path)"
  

  Reload your shell with source ~/.zshrc (or the appropriate file), then install Python 3.6.5:

  pyenv install 3.6.5
  pyenv global 3.6.5 # Set this as your default system Python
  

• Miniconda/Anaconda
  Perfect for data science workflows—comes preloaded with popular scientific libraries. Download the lightweight Miniconda installer, run it, then use conda to manage your Python environment:

  conda create -n py36 python=3.6.5
  conda activate py36
  

A quick note: Avoid running brew with sudo unless it's absolutely necessary. It causes files to be owned by root, which leads to ongoing permission issues like the one you're facing. Fixing directory ownership is the safe, recommended approach from the brew team.

内容的提问来源于stack exchange，提问作者joesan