It has nothing to do with your actual age.
e: To clarify for non-native-English peeps, where I come from we use the term "old fart" to describe someone who complains a lot and is resistant to change, it doesn't matter if they are 18 or 80. It's not normally considered very offensive, no more than say calling someone a dork or poo poo face.
>native Brit here. I can confirm that it is about the resistance to change more than age and hardly ranks on any scale of offensiveness I consider worthy. To give another example, good ol' boys aren't necessarily old either, of course. (Dukes of Hazard lol)