You are kidding right? There are many tools available that will allow you to do exactly that, including the free Google Analytics. Talk to who ever maintains your website, they should be able to provide you with several options that will fit your budget and needs.
Perhaps he is arguing, and I may be reading too much into this, that once you have hit free as a price point, you have removed price as differentiator and now must compete on value. If he is, it is a weak argument as you can always be undercut.