Just to add a small little bit to what everyone else said, the user may map to the login with a different name. For example, the user may be named "user1" whereas the login is "login1".
On top of that, the login may map to users in multiple databases. So unless you ONLY have 1 user database, dropping the login may result in orphaned users on other databases in that instance.
If you REALLY need a stored procedure for dropping a login, I would recommend using a loop and dynamic SQL query to go through each database to drop the USER on each database prior to dropping the login as it is easy to map those 2 together WHILE the login still exists. Once the login is gone, you may end up with orphan users in other databases that will be tricky to fix as it is hard to determine which are orphaned and which are intentionally users without logins.