I can login with same username in different browser.

that is possible coz cookies are at different directories for the diffrent browsers.
same will happen with gmail. yahoo, orkut, hotmail. or anything..

This does not happen now in facebook and gmail i have tried it..
they logout the first one automatically..
how every you can login with different user name in diff. browser
BUT
you can login with same user name in diff. browser in jcow script

In facebook if you login from another browser then session for older browser is gone. And shown a confirmation to login.

is this really a bad thing?

Look at Google, Yahoo, Facebook, etc. All of them use single login...

Maybe the problem is in security. I don't know much about security.

if people are worried about the security of their account then surely they would log out?

Hey, if you're a programmer you should know this. A programmer must handle all of chance user may do.