To do this, he acquires a nuclear launch control device, which we'll assume is code named "Joshua" and can be deactivated by forcing it to play a game of tic-tac-toe. During the climax, Hendricks uses the device to fire a Russian nuclear missile at San Francisco before tucking the device inside his briefcase. Ethan Hunt chases Hendricks to the upper level of a parking garage, where, with only minutes left until the missile strikes, Hunt barks out, "I'M TAKING THAT BRIEFCASE." Hendricks responds in the only way he logically can: by leaping several stories to his death, taking the briefcase with him.
Wait a Second ...
Couldn't he have just, you know, tossed the briefcase down there? There was no reason to toss himself along with it, unless his feelings were just really, really hurt by Hunt's rude outburst.
"How dare he offer such impertinence! And while looking so inexplicably youthful!"
Hendricks' strategy is to keep Hunt away from the device long enough for the missile to strike San Francisco. He's willing to sacrifice his own life for this plan, which is commendable, but also entirely pointless. Hunt doesn't care about catching Hendricks at this point, he just cares about the device -- Hendricks could have simply thrown the briefcase down there and tucked away a few levels of Candy Crush while Hunt sprinted off to try to catch the thing in time.