Half of the people in the world are aged 25 or under; so if you're 26 or over, you are in the 'old' half of the population!
I hate the way that being 'old' is automaticaly considered such a negative thing, when it comes to humans. MN is especially weird with this, insisting that you're just approaching the very beginning of middle age at 65.
'Old' doesn't only mean that you're biologically nearer the grave than the cradle, but It also carries a natural understanding of having acquired experience, wisdom, knowledge, maturity etc. in a great many cultures. The idea of a 'village elder' is a really positive one; not pejorative or dismissive at all.
I agree that it's partly a mindset and partly individual circumstances. It's also not a competiton or a hierarchy. Saying that you are/feel old - often in a jokey manner - isn't the same as claiming to be the oldest person who ever lived. Most people wouldn't quibble for a second that an 80yo is 'old' - yet there are people out there who are 25+ years older than they are!
As PP said, if you're a parent - especially to little children - it really does set the scene that you are/feel 'old' in comparison. When you see them starting to grasp and deal with the most basic things that you grasped or left behind decades ago, I think it does put things into perspective more.