"It also assumes that you're two-dimensional."
From Lewis: "... it assumes that healthy weight should scale up in relation to the square of height - a patently absurd idea, ..."
The square of height thing seems to assume that we're modelled as a cylinder, which is not a bad approximation - and that's all it is, an approximation to let a doctor/nurse or yourself obtain a quick and easy measure for comparison purposes. It's also only appropriate for someone around average height and build, not a particularly tall or muscular man or woman.
The last time my doctor had a good look at me (almost naked), she said I could do with having a bit more weight. I pointed out that my BMI was 23 and she went very quiet. I didn't point out that she was a bit of a porker and that people tend to want to see themselves as 'normal'.