I don't think he was an idiot ,I just think he thought the defense was playing well in the second half and he thought his defense would force a turnover or a 3 and out and it would lead to an easy Field Goal attempt by Gostkowski.Either way it was a terrible idea but I'm glad he did it,If he didn't we might not be in the situation we are in
That rational makes you an idiot if that's what he was thinking. He played to win the game but at that point in seeing the Steelers losing, I think Belichick saw an opportunity to eliminate the only other elite quarterback in the AFC playoff race by giving the Jets the opportunity to win. Any other rational makes absolutely no sense because you never ever ever ever ever elect to kick in overtime.