Black 1 kills by nakade. There's no way White can make two eyes now.
If , makes an eye in the stomach. If White does play inside the group, Black can fill all outside liberties and eventually atari at either a or c. If White next plays a or c, Black b makes a rabbitty six inside White's eyespace.
Black 3 here is a mistake. turns the position into seki.
In both cases, White is able to take the vital point.