Why when you put a suffix 'en' at the end of word 'te' the 'e' letter of the word 'te' remains? And we write the word 'the tea' with 2 e's (tEEn) and not with one 'e' (ten)? Because, for instance in definite form of word 'coffee' (en kaffe) we only have one 'e' left - kaffEn.
It has to do with how the words are pronounced: "tE-En" and "kaff-En".
"Teen" retains the e from its stem, because it's actually pronounced.
It's not referring to tea in general, but rather to a particular type or cup of tea.
Any respectable Briton should be particular enough about their tea to sympathise. ;)