Isn't that something we hear a lot? It might be an Old Wives Tale, but it's repeated both as an allegory for people who don't want to change... and it's equally used to prove that you MUST have a dog as a puppy to be able to train them properly.
One of the problems is that if you've had a dog for a long time, you're in a rut or in a routine. Your dog knows exactly how you're going to react, they know how serious you are when you ask them something, and you probably do the same old thing.
A lot of human relationships end up like that!
If it really were the case that "you can't teach an old dogs new tricks" then there would be no point trying to rescue any dogs older than a puppy.
There are thousands, maybe even millions of rescue dogs out there that are happy in their new homes and learning new stuff all the time. And what age does a dog become an 'old dog'. At what age are we supposed to consider the cut-off point for learning?
For some rescue dogs, we don't even know their ages. So we can't exactly apply a cut-off point. And any such limit would be artificial anyway - it just gives the person dealing with the dog a reason not to pay attention to them.
You see older folks in the coffee shop bashing away on their tablet computer or smartphone, zapping around apps like they are second nature, and others who can't. It isn't about age. Sometimes it's about a state of mind, and the reasons to want to learn.
You can continue working with problems all the way through a dog's life; it doesn't matter how old a dog is, but it's how you understand that dog. If you're trying to change an unwanted and deeply ingrained behaviour, it's all about understanding what drives and interests the dog in front of you.
Working with older dogs can sometimes be easier than working with the young ones. They concentrate better, and aren't always as easily distracted. You may have to work harder at gaining their respect to start off with, but the rewards are there if you're willing to put the time and effort in.
You can teach an old dog new tricks - but the humans need to keep learning too...