エラーメッセージ
Error: parent directory is world writable but not sticky
Please report this bug:
https://docs.brew.sh/Troubleshooting
/System/Library/Frameworks/Ruby.framework/Versions/2.3/usr/lib/ruby/2.3.0/tmpdir.rb:93:in `mktmpdir'
/usr/local/Homebrew/Library/Homebrew/extend/pathname.rb:167:in `atomic_write'
治し方(結果論ですみません)
$ sudo chmod +t /private/tmp
$ sudo chmod +t ~/Library/Caches/Homebrew
を実行したら治りました。
ソース元
https://stackoverflow.com/questions/42893700/error-parent-directory-is-world-writable-but-not-sticky