There's been a lot of discussion about Lieberman's behavior during the election, from suggesting Obama might be a Marxist to accusing him of "not putting country first," to other assorted incidents in which Lieberman embarrassed himself while shilling for John McCain. But none of those are reasons why Lieberman should lose his chairmanship of the Homeland Security Committee.
Lieberman should lose his chairmanship of the Homeland Security Committee because it's about to be 2009 and there is no reason to keep an anti-Muslim bigot who believes the United States is being subverted by Muslims from within in charge of a Committee that handles national security affairs. Lieberman participated in The Third Jihad: Radical Islam's Vision For America, a movie which claims there is a vast conspiracy of American Muslims to subvert democracy ... and has a secret FBI file to prove it, just like African Press International has an interview with Michelle Obama they are selling to FOX and Larry Johnson has the Whitey Tape. These are the same people who gave us the shadowy anti-Muslim Obsession film that was distributed in newspapers in swing states during election season.
Put simply, you can't have an anti-Muslim bigot in charge of Homeland Security when the country as a whole is dealing with the threat of Islamic extremism. The reason you can't have a bigot in charge is that a bigot can't tell the difference between normal Muslims and extremists. Lieberman is simply incapable of doing his job correctly. He is a security risk.