I think the three-and-ten, four-and-ten way of expressing numbers is primarily an ancient Greek thing. The modern numbers are expressed differently (δεκατέσσερα / dekatessara for fourteen, for example). In a lot of older European languages 11 and 12 behaved irregularly. You could argue that they do in English too (we don't have oneteen and twoteen).

I haven't read of any particular reason for this, but I'd posit that numbers up to twelve were more commonly used in everyday life, so shorter, irregular forms were easier to use and remember. Much like many of the irregular verb forms in spoken language happened because they were so commonly used.

The ancient Greek system also gave us triskaidekaphobia - the fear of the number 13.

Indeed, in ancient greek they put the "δέκα" (ten) part second. Τρία και δέκα (13), τέσσερα και δέκα (14), πέντε και δέκα (15), etc, but 11 and 12 was (and still is in modern greek) irregular, έντεκα (enteka) and δώδεκα (dodeka) respectively.