Your question is not really appropriate to this section which applies to scientific theories of elementary particles beyond the Standard Model. Your question should rather be posted under Philosophy or General Discussion.
But to answer your question, firstly there's no reason it couldn't be otherwise and there have been in past "decimalization" movements suggesting alternatives especially 100 "seconds" to a "minute" etc, and 10 months to a year. See http://en.wikipedia.org/wiki/Decimal_time" in wikipedia and check out the related topics.
You're question would be better answered if you did a little history research and contemplation as to why we have the systems we currently use.
One common reason for using divisions of 12, 24, and 60 parts is it is easily divided into small increments, i.e. halves, thirds, quarters, and sixths, etc.
A 24 hour day for example is useful in dividing watches on ships into 6 four hour watches, http://www.boatsafe.com/nauticalknowhow/shipbee.htm" . That'd be tougher with say a 17 "hour" day.