First, now that you've provided more information, I understand why your user needs an ODBC connection. And yes he does need one. Your original post never said anything about a third-party application being used. Since you hadn't said anything about the 3rd-party app I assumed he was using Enterprise Manager or Query Analyzer.
So, let me start over...What is the SQL Server authentication set for? Go to Enterprise Manager, drill down to the server and right click on the server. Select Properties and go to the Security tab. What is the Authentication set for (SQL Server and Windows or Windows Only)? I'm guessing it's set for Windows only. If so, he will have to change that or use Windows Authentication in the ODBC connection.
Now for your question. Do you have an account (login) in SQL Server? What permissions do you have with that account? Use Enterprise Manager, drill down to Security, click on Logins. Find your login, right click and select Properties. Go to the Server Roles tab. Do you have Security Admin privileges? How about System Admin privileges? You need one of those to change/add/modify logins.
-SQLBill