Why can't I change system time to less than 1970?

UNIX and POSIX-compliant systems encode system time ("Unix time") as the number of seconds elapsed since the start of the Unix epoch at 1 January 1970 00:00:00 UTC, excepting leap seconds which are not counted. The limitation was inherited from UNIX. 32-bit values meant, to get a reasonable degree of precision, Day Zero had to be pretty close, so that precluded going back to 0 A.D., or, more reasonably, 5780 years and change, since the date of this answer is 10 Adar 5780 {g}.

From the wikipedia:

Unix time (also known as Epoch time, POSIX time, seconds since the Epoch, or UNIX Epoch time) is a system for describing a point in time. It is the number of seconds that have elapsed since the Unix epoch, that is the time 00:00:00 UTC on 1 January 1970, minus leap seconds.

Also an explanation:

Linux is following the tradition set by Unix of counting time in seconds since its official "birthday," -- called "epoch" in computing terms -- which is Jan. 1, 1970.

A more complete explanation can be found in this Wired News article. It explains that the early Unix engineers picked that date arbitrarily, because they needed to set a uniform date for the start of time, and New Year's Day, 1970, seemed most convenient.