You must have already seen a lot of facebook users do it. You tried logging into two different Facebook accounts, but some how your browser was not allowed by the facebook server to get through , but why ?
The reason is simple. Facebook server tracks cookies in a browser for a user to stay active. Only one user can stay online at a time without logging out. But you can log into two different facebook accounts simultaneously using two different web browsers for two different accounts, ie. login to facebook with one account using Internet Explorer, which is a part of your Windows OS installation and with Mozilla firefox on the other side. You can download and install firefox and use firefox to login to the second account. If you can use more browsers like Opera, you can login to facebook with more accounts.