Why are teens "teens"?

The word 'teen' is merely a variation of the word 'ten'.

'Thirteen' is a way of saying 'three and ten' from the Middle English thrittene which itself is from the Old English threotine.

Some people mistakenly believe that 'teen,' short for 'teenager' has something to do with the obsolete word 'teen,' meaning misery or affliction, but that is not so. The two words merely share a coincidental spelling.

Check out the last article on this page from The Word Detective:

http://www.word-detective.com/042805.html

I suspect teen is a modification of ten or tyne.

thirteen = three + ten

fourteen = four + ten

sixteen= six + ten

That's what it is in French, which English is partly (a good chunk) based on. E. g., after 16 and before 20, the numbers are
dix-sept (17, or, literally, 10-7)
dix-huit (18, or, literally, 10-8)
dix-neuf (19, or, literally, 10-9)

Is it the same in Latin? George or contrex would know.

Well, it's pretty alike, except the position of the parts:

10 dĕcem
11 undĕcim (one+ten)
12 duodecim (two+ten)
13 tredecim (three+ten)
14 quattuordecim (four+ten)
15 quindecim (five+ten)
16 sedecim (six+ten)
17 septemdecim (seven+ten)
18 duodēvīgintī (two out from twenty)
19 undeviginti (one out from twenty)
20 vigintī

A link in French, Jespah, for Romance languages :Numbers

Seventy is "soixante-dix" in French, ("sixty and ten"), Eighty is "quatre vingts" (four twenties or "four score" if you like), and ninety is "quatre-vingts-dix", (four score and ten).

The numbers above sixty-nine seem to "break the rule". Up to about the 15th century they didn't, but the French used in France evolved. But go to French speaking Belgium, Luxembourg and parts of Switzerland (Not to mention the Val d'Aoste in Italy) and folk still say "septante", "octante" and "nonante".*

*Une variante vaudoise «noinante» s'entend encore chez les gens âgés...

It's actually much closer to German than one thinks

13 - Dreizehn (three ten)
14 - Vierzehn (four ten)
15 - Fuenfzehn (five ten)
16 - Sechzehn (six ten)
17 - Siebzehn (seven ten)
18 - Achtzehn (eight ten)
19 - Neunzehn (nine ten)

French number oddities...

you say vingt-deux, quarante-deux, soixante-deux,

but you say vingt-et-un, quarante-et-un, soixante-et-un.

dates: when you say or write the 11th of any month, it's le onze (mai, juin, septembre, whatever) even though "onze" starts with a vowel.

12 and 20 are numbers which historically have their own special words, "dozen" and "score" respectively, though the latter doesn't seem to be used much anymore. 13-19 are the whole numbers in between, no more, no less, and they are the only ones with "teen".

Well I can honestly say Ive learned something today.....thats a rare occurence.