The cells that you need to make hairs are not present on your tongue. It does have hairs of sort – they are called microvilli, and are needed to sense things, help create a food bolus and prevent you from swallowing your own tongue
This is difficult to answer without falling into a particular problem with “design” arguments … oh well, let’s fall right in 🙂
If tongues were hairy, it could be very difficult to clear our mouths of food, as it would get matted in the hair. Keeping the mouth slick is the job of saliva, but it is greatly helped by having the insides of our mouth smooth. Why do we want to clear our mouths quickly? – because we need the nutrition inside us; we don’t have time to hang about eating when there’s work to be done, or when some beast bigger than us is out to steal our meal. Any hairy-tongued mutant would have spent too long eating, missed out growing big and strong (when in competition with his less-hairy brothers and sisters), and hence have been less successful at mating. Perhaps she enjoyed her food more – a transient consolation, but an evolutionary dead end.
So, how is it that hairs don’t grow on tongues (i.e. how does the body build itself so hairs don’t grow there)? Hairs form from hair follicles. Hair follicles are made up of special cells that will only form in certain tissues. So, somewhere within our genetic code (we don’t know where) there is no instruction that reads, “if you find yourself growing in a tongue, consider turning into a hair follicle” … or something like that!
By the way, I have been thinking that having hairs inside out mouths might have one use – to get a better measure of the viscosity or stickiness of foods – I guess that we can do well enough without them!