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.

On a UNIX (and Linux) system, the counter for the time is interpreted as an unsigned value of (milli)seconds, and zero is defined as 1970-01-01T00:00:00.000 UTC. If you want to set the system time to any date/time before that, you would have to set that counter to a negative value – something that does not work for an unsigned value (as it is unsigned …).

There are several explanations around why the creators of UNIX chose that point in time for the 'Begin of the Epoch', and I have no clue which one is correct. But their decision for 1970 is the reason why you can't set your system to an earlier time.