os 10.11.6 pip install permission error
Do NOT remove your Apple system provided python version found at this path:
/Library/Frameworks/Python.framework/Versions/2.7

In fact - you should never mess with any Frameworks under /Library/... unless you know what you are doing.  Your OS may have tools that depend on this version of Python that it ships.

After installing brew - did you run


  brew doctor


It should tell you if you have any issues.

Also - be sure your brew install python3 (note there is not a space - 'python 3')

After installing your new Python - brew should put it under /usr/local/ not /Library/...

I suggest you use either Homebrew or Macports - NOT both.  Make sure you follow the directions on their webpages and set your PATH in your .bashrc or .bash_profile properly.

After you set your PATH in those files, don't forget to "source" the files - or simply close and reopen terminal to "refresh" your environment to the new settings.

Good Luck!