I read somewhere that when you're younger, you learn much better and faster. So for example, if you took up a language or a sport when you were 10 years old and stuck with it for years, you'd be really good at it by the time you were 20. But if you take up that same thing at 20, you won't be as good at it by the time you're 30. Basically the older you get, the harder it is to become good at something.
Is there any truth in this and is it a justifiable reason to not learn anything new past a certain age?
Adult learners easily compensate though by having a far better approach and more developed learning techniques.
There is definitely some truth in it. If you even consider language, with all its extremely complex syntax and semantics rules, its pretty evident that children have amazing learning capabilities. I'll mainly consider intellectual skills here. A child's brain is fresh, it is ready to form new connections and can become hardwired to have exceptional potential in a skill. Assuming both don't have much mathematical training, for example, it is definitely easier for a 10 year old child sitting down to learn maths (seriously, almost religiously) to become an exceptional mathematician than it is for an adult putting in the same effort. The child will probably be a genius (eventually), the adult probably won't but can still be very good with hard work. Look at people like Turing, Hardy, Von Neumann, Gauss, Riemann, Euler, Neil deGrasse Tyson, Michio Kaku, Stephen Wolfram, Terence Tao. You can sit down all day and keep searching for exceptional thinkers - virtually all of them started young.
Speaking from a personal perspective, I'm 18 and trying to become a brilliant mathematician, but I only got serious about learning it at 16, so as much as I want to be a genius I will probably never achieve that because my brain's wiring is a lot more fixed and will take much, much longer to adapt. This doesn't mean all adults shouldn't try to be exceptional at something, I believe everyone should keep learning and improving until the day they die! But there is definitely more of a limit put on you the older you become in my opinion.
I've mainly looked at maths here, I know, but I'm sure the same thing applies to most other intellectual fields too.