Philosophers have, in general, kind of muddied the waters there -- job security. But "analytic propositions" basically follow from that concept of "by definition". For example, "all teenagers are 13 to 19", is an example of an analytic proposition because it is "true by definition". If someone is 13 to 19 then "she/he/it" is a teenager. And if they're not 13 to 19 then they're not a teenager. No exceptions.
You keep using this example but it's actually a terribly vague and inconsistent definition. Is a 17 year old cat a teenager? Is a 13 year old sea tortoise a teenager? How about a 15 year old giant sequoia tree? If I said "look at that teenager" while pointing to a bowl of Jell-O that was forgotten in the back of the fridge for nineteen years, do you think the person I was speaking to would just be grossed out, or confused
and grossed out?
Don't try to give me any nonsense about "teenager" only applying to humans. You've been quite firm that definitions are completely invalid if they don't apply to every possible species.
In fact, "teenager" should apply even more broadly than that, because only living species reproduce with gametes but all kinds of things have an age. Was the Moon a teenager thirteen years after it formed? Is a fifteen year old toaster a teenager?
But the questions and problems don't end there. Fictional characters are among the many things that can have an age, and it's well known that they can be teenagers. Let's consider one example. Any film critic summarizing the plot of
Ferris Bueller's Day Off will note that Ferris, a high school senior, is a teenager. Now, it's well known that the actor playing Ferris was 23 at the time. That's no problem because it's the character who's a teenager, not the performer playing that character. The actual problem is that the character was created in or before 1986. That is to say, the character is at least 38 years old. So, a teenager and yet not a teenager. Completely inconsistent!
This can be true of real individuals as well. Pharaoh Tutankhamen ("King Tut") was nineteen (or possible eighteen), a teenager, when he died, according to forensic and archaeological consensus. But that was over 3300 years ago. Is he still a teenager? If so, how is that possible being over 3300 years old? If not, how did he age after death? Why do all the signs at the museums call him the "boy king" instead of the "incredibly old man king?" This isn't just an issue for ancient kings. Should we stop referring to the "teenage victims" of the Columbine shootings, because they're all middle aged or older now? No exceptions, remember!
Can hard physical science clear this up? Let's see. Well-established relativistic physics tells us that if an 11-year-old space cadet were to away on a spacecraft making a round trip to a distant star at high relativistic speeds, the cadet might have only aged four years despite 100 years passing on Earth upon his return. So at the end of the trip he's a teenager in ship time but way too old to be a teenager in Earth time. That's no good.
A proper scientific definition must apply at every velocity! No exceptions!
Then, consider what it means if it turns out after the stowaway was discovered aboard the space ship he was put in cryo-stasis for the first three (ship time) years of the mission, to save resources. So physiologically he's only aged one year between his departure and his return, too young (by that measure) to be a teenager yet. So in that case he's simultaneously too young, too old, and the right age to be a teenager.
Clearly your definition of teenager is completely inadequate, and using it can only result in confusion, conflict, overly lenient home mortgage lending policies, and a pestilence upon the land. Two pestilences and a heavy fog, even.