This objection never made too much sense to me. In the standard model of perfect competition, firms take the price as given and respond by choosing their quantity. So you have a model in which a bunch of actors choose quantity and the market price emerges as a consequence of all of those decisions. This makes it sound awfully like price is the "dependent" variable, which by convention is always placed on the vertical access.
Indeed, this seems to be how Alfred Marshall (who originated the modern form of the Demand-Supply diagram) thought about things. Here's a quote from An Introduction to Postitive Economics, Seventh ed. by Richard G. Lipsey (as quoted here):
"Readers trained in other disciplines often wonder why economists plot demand curves with price on the vertical axis. The normal convention is to put the independent variable on the X axis and the dependent variable on the Y axis. This convention calls for price to be plotted on the horizontal axis and quantity on the vertical axis.
"The axis reversal - now enshrined by nearly a century of usage - arose as follows. The analysis of the competitive market that we use today stems from Leon Walras, in whose theory quantity was the dependent variable. Graphical analysis in economics, however, was popularized by Alfred Marshall, in whose theory price was the dependent variable. Economists continue to use Walras' theory and Marshall's graphical representation and thus draw the diagram with the independent and dependent variables reversed - to the everlasting confusion of readers trained in other disciplines. In virtually every other graph in economics the axes are labelled conventionally, with the dependent variable on the vertical axis."
See also this post on Greg Mankiw's blog.