reinstall: handle remove/rename permission errors.

Library/Homebrew/formula_installer.rb

@@ -289,7 +289,14 @@ class FormulaInstaller
       rescue Exception => e # rubocop:disable Lint/RescueException
         # any exceptions must leave us with nothing installed
         ignore_interrupts do
-          formula.prefix.rmtree if formula.prefix.directory?
+          begin
+            formula.prefix.rmtree if formula.prefix.directory?
+          rescue Errno::EACCES, Errno::ENOTEMPTY
+            odie <<~EOS
+              Could not remove #{formula.prefix.basename} keg! Do so manually:
+                sudo rm -rf #{formula.prefix}
+            EOS
+          end
           formula.rack.rmdir_if_possible
         end
         raise if ARGV.homebrew_developer? ||

Library/Homebrew/keg.rb

@@ -310,7 +310,7 @@ class Keg
     remove_opt_record if optlinked?
     remove_old_aliases
     remove_oldname_opt_record
-  rescue Errno::ENOTEMPTY
+  rescue Errno::EACCES, Errno::ENOTEMPTY
     odie <<~EOS
       Could not remove #{name} keg! Do so manually:
         sudo rm -rf #{path}

Library/Homebrew/reinstall.rb

@@ -45,12 +45,26 @@ module Homebrew
     ignore_interrupts { restore_backup(keg, keg_was_linked) }
     raise
   else
-    backup_path(keg).rmtree if backup_path(keg).exist?
+    begin
+      backup_path(keg).rmtree if backup_path(keg).exist?
+    rescue Errno::EACCES, Errno::ENOTEMPTY
+      odie <<~EOS
+        Could not remove #{backup_path(keg).parent.basename} backup keg! Do so manually:
+          sudo rm -rf #{backup_path(keg)}
+      EOS
+    end
   end
 
   def backup(keg)
     keg.unlink
-    keg.rename backup_path(keg)
+    begin
+      keg.rename backup_path(keg)
+    rescue Errno::EACCES, Errno::ENOTEMPTY
+      odie <<~EOS
+        Could not rename #{keg.name} keg! Check/fix its permissions:
+          sudo chown -R $(whoami) #{keg}
+      EOS
+    end
   end
 
   def restore_backup(keg, keg_was_linked)