Wednesday, June 13, 2012 - 7:25 PM CDT
Hi, Jeremy-- The short answer is that he doesn't want to be followed.
That said, here's the way I see it. Peter (Kirk Douglas) and Childress were colleagues who admired each other, and now, of course, hate each other's guts. Peter has been on the run from Childress for many months, and has had to outwit him to stay alive as he searches for his son (Robin). Since each of them (Peter and Childress) is very very good at what they do, this has resulted in sort of a game of one-upmanship between the two, with the stakes particularly serious for the desperate Peter.
The one-upmanship begins in the film's opening sequence, when Peter rises from the water and shoots Childress' arm. He then makes his escape-- thought dead, Peter becomes a ghost, and a thorn in Childress' side, albeit one he treats with disdainful respect. Before driving the car into the river, Peter establishes himself with the cops as rather insane, even though all he does is tell them the truth. He gives them a verbal message to give to Childress before he drives off, sounding even crazier, and with a crazy look in his eyes. Peter has made it look as though he decided he can't take the constant surveillance and paranoia anymore. Knowing that Childress himself will be there to see whether or not Peter is in that car when it is raised out of the water, he relishes imagining the look on Childress' face when the car comes up with no body inside.