Because decimal math sucks at halfing and doubling in even increments. Ten can be factored into 1, 2, 5 and 10, of which only 2 can be evenly halfed again with another whole number. Twelve can be factored into 1, 2, 3, 4, 6 and 12. Sixteen into 1, 2, 4, 8, and 16.
Yes, 12 can be divided evenly into halves, quarters, and thirds. That is an advantage when counting by whole numbers. (I score quizzes on a 12-point scale; that way, I can easily grant partial credit in whole-number steps.)
Whatever the advantages of a traditional duodecimal system for counting, it has no such advantages for measuring or calculations. There are two reasons for this.
First, most of the traditional systems of measurement are not based on 12. Yes, there are 12 inches in a foot; but there are three feet in a yard, 1760 yards in a (statute) mile, and so forth. Likewise, none of the traditional units of mass, weight, volume, area, etc., are based on divisions of 12.
Second, we calculate using base-10 numbers. Having units that are also based on 10 greatly simplifies calculations and reduces the chances for error.