An enthymeme is a matter of logic.
To get an enthymeme you have to start with a syllogism. A syllogism is a statement where you deduce a fact as a result of stating and then accepting two others.
Dogs are mammals.
Snoopy is a dog.
Therefore, Snoopy is a mammal.*
If you don't bother to state one of the supporting facts then you've got an enthymeme:
Snoopy is a mammal because he's a dog.
But there are other types of enthymeme, and some of them are very weak indeed. You can have an enthymeme which relies on a sign of something to bring you to a conclusion:
She's wearing fur, therefore she's not a vegan.
which is usually true - but not, for instance, if the she in question is a hamster.
Weaker still are the enthymemes which are based on prejudice - though these do come in very useful for jokes:
I can always tell when my mother-in-law's coming to stay: the mice throw themselves on the traps.
It may take a while to unpick the logic in that statement, but over the years it's still made a lot of people laugh.
Thing To Consider Today: enthymeme. The Greek word enthumeisthai means to infer, from thumos, mind.
*Which just goes to prove that even logic isn't necessarily completely bullet-proof.