Qaddafi loyalists' fight "does not make sense"

In the battle for Libya, a NATO spokesman said Tuesday: "It does not make sense" that Qaddafi loyalists are still fighting in his hometown, Sirte.

The former rebels have the loyalists surrounded. CBS News correspondent Allen Pizzey reports the fight put up by the remaining Qaddafi fighters is fierce.

Scenes in the video above show groups of former rebels facing off against a sniper killing ground.

The battle for Sirte is being fought with small groups of men answerable to no one but themselves, trying to advance to a front line they can't define, shooting at the enemy they can't see, trying desperately to close the noose on Qadaffi's last holdouts.

In yet another bizarre twist in this war, CBS News came across an American manning the anti-aircraft gun. Matthew Van Dyke came here in March to fight alongside a Libyan friend, was caught by Qadaffi's men, and escaped when Tripoli fell.

"I came to this country willing to kill people for freedom. Yeah, it's something that I struggle with. You know, and I hope I don't have to kill anybody. Maybe I just did. I don't know," said Van Dyke, who is from Baltimore.

The noise and intensity of the battle is so great that, even if Qaddafi's men offered to surrender, no one would hear them.