...This is sometimes used to relate the liar's paradox in logic. Overly pedantic intellectual types like this anecdote because of its reference to some sketchy historical facts from BCE. St. Paul (Christian testament writer) also alluded to it once, but possibly for slightly different (though related) reasons.
Today, the Cretan is used only to relate the concept. This, in turn, tends to cause us (as humans) to get caught up in the human aspects associated with other people. That confuses the actual issue by opening the door to a lot of straw men...
Another way to give example of the liar's paradox (sans the human from Crete and his community) is in a simple sentence:
This statement is a lie.
I have seen philosophical/semantic analysis of this, which claim to prove it is not "really" paradoxical. I can't say for sure if those analysis are correct because I have not been able to follow them to the end. Reason? About halfway through, it becomes clear that the whole claim rests on the notion that this is a single statement. That, in turn, makes the argument moot since the paradox could have just as easily been related like this:
The next sentence is a lie.
The previous sentence is true.