The issue is, human drivers have a strong instinct of self-preservation. Someone who has to decide between the parade and the tree in a split second will probably avoid the tree out of sheer instinct.
Now then, you might think the cool-headed computerized car will make the right decision and kill its occupant. But I can just imagine the following court case: "Your honor, my father's car killed him wilfully. I therefore sue Toyota/BMW/Honda/Google for murder, and for 100 kajillion dollars in damage".
One such court case - especially in the US - will do enormous damage to the entire industry, and might kill it off entirely. And no, the argument that autonomous car create fewer accidents overall won't fly, because somebody's property isn't supposed to kill its owner on purpose. You can bet emotions will run high, and emotions aren't good for rational debates.
Not to mention of course, people will have second thoughts about buying a vehicle that they know can decide to put them in danger for the greater good.