Cricket is so backwards.
You mean using tech to get to the right decision?
Ignore the caught behind. The umpire gave him for that and it was not out.
Hawkeye has a margin for error. Therefore if it's within that margin for error, they base the decision on the umpire's original decision. The umpire did not give him out LBW originally. Therefore when the ball was within the margin for error, it was not given out correctly.
What's wrong with that?
Edit: I take Gilly's point that the umpire didn't have the option to give him LBW as well - however, the umpire believed he had hit the ball. He therefore couldn't have then said "I think it's LBW" without coming across as an idiot.