Why should dynamical downscaling of meteorological data be made incrementally?
The basic answer to your question is that there needs to be an overlap between the spectra of the two domains. One way to think about it is that there needs to be a connection between the Kolmogorov energy cascades (https://en.wikipedia.org/wiki/Energy_cascade) of the two domains. 

Kolmogorov energy cascade (D. Newman, U. Alaska Fairbanks).

Each domain is going to be forced (have energy input) at a relatively large scale and it is going to assume that the energy that it can't resolve at sub-grid scales is going to be dissipated. If there is no (or little) overlap between the two grid resolutions, the energy from the large domain (parent) will be dissipated by viscosity at sub-grid scales that the small domain (child) cannot resolve and there is not going to be an appropriate input of energy from the parent to the child. 

The reason for the odd numbers in the ratio is given in Why is WRF most often configured at 3:1 nesting ratio?