Why does the load resistance has to be >100*Source resistance in case of a stiff voltage and <0.01*Source resistance in case of a stiff current?
The question is asking why we need a large ratio between source resistance and load resistance.

There are two cases to consider. We could have a low impedance voltage source (ideally a zero impedance voltage source) driving a high impedance (ideally open circuit) load.  We could have a high impedance current source (ideally infinite impedance) driving a low impedance (ideally short circuit) load. 

The ratios suggested in the OP's book are for at least 100:1. 

It doesn't have to be those ratios. 

But if it is, the error due to loading compared to an open circuit (for a voltage source) or a short circuit (for a current source) will be 1% or less. 

If the ratios are 0.001, then the error be less than 0.1%.

If the ratios are 0.1, the error could be up to 10%.

I guess most people think 1% is somewhere in the ballpark of a negligible error. If you have different error thresholds, then you'll want to use different ratios.