Simple. He wants to die. In the extremist Islamic belief, he would die a hero martyr. He wants the glory and the open arms of Allah. If we excute this man, he would be guarenteed a place in Allah's "heaven", according to his belief.
He does not, however, want a sentence of life in prison. There would be no glory in getting raped, beaten and tortured by American inmates for years to come.
That is why he is practically taunting the judge, prosecution and jury. He's daring them to kill him.
This man needs to live.