No, you do not start counting things at zero. Because at zero that thing you are trying to count doesn't exist. If I put five rocks in front of you and ask you to count them, you don't point at each rock and say "zero, one, two, three, and four".
The stupid part of all this is that typically if you request the length of the array of our rocks, you will get five. But request the index of the last entry and you will get four. The simple fact that to refer to the last index in the array you have to use something like array.length - 1 points out the silliness of the whole thing.
EDIT: After a moment I felt the need to add that I'm not necessarily saying that all arrays need to start at one over zero, it's just that the whole thing is silly on first appearance. If the reason to start at zero is technical then fine, but as frustrated developers we have to have something to complain about.