Cygwin mkdir makes directory I don't have permissions to
The excess of DENY showed by icacls can be caused by the recent changes in cygwin dll (between 2.3 and current 2.5) . It took some round to be right and could have left files or directory with puzzling ACL.
To sanitize the ACLs, a -b switch was added to setfacl
setfacl -b foo
For reference https://cygwin.com/cygwin-ug-net/ov-new.html#ov-new2.4s