Why is zener current preferred to be more than load current in a voltage regulator?
No such condition exists.  The only restriction is that the current thru the zener diode be within its specified range so that it develops the desired voltage on the low end, and not dissipate too much power on the high end.  As long as this condition is met, the voltage will be regulated.

Added:

I see from the comments that there is still some confusion.  Let's do a example that proves the stated restriction does not exist.  Suppose we have a zener that regulates to spec over the range of 1-20 mA.  Put less than 1 mA thru it, and its voltage will be too low.  Put more than 20 mA thru it and it blows up.

Now imagine that Rs is sized so that the maximum 20 mA flows thru the zener when there is no load.  This means that 20 mA always flows thru Rs as long as the voltage is being regulated.  The load can therefore draw anywhere from 0 to 19 mA with the voltage staying regulated.  The zener current will be 20 mA minus the load current.  You can see that there is quite a range where the load current can exceed the zener current, with 1 mA thru the zener and 19 mA thru the load being the extreme case.