Why fully cycle Li-Ion laptop battery?
In my opinion the advise of the laptop's manufacturer (to fully cycle the battery every time) contradicts general concensus that many partial charge/discharge cycles prolongs battery life.

See the tables on this page at Battery University

Maybe the battery in your new laptop is not a standard Li-Ion based one but I doubt that. If you add the brand and model of the laptop in your question we can maybe further investigate this.

But it looks to me as if that laptop manufacturer does not have a clue and is advising you something that is actually going to make your laptop's battery wear out sooner !

The explanation why partial discharges are better is that a very low or very high battery voltage (that voltage is proportional to the battery's charge level) puts a lot of stress on the battery. By keeping the battery voltage near the middle or around 50% to 70% charge level puts less stress on the battery making it last longer.

BTW it is recommended to do a full charge - discharge cycle every now and then, like every 3 months or so. This is not for benefit of the battery but for the charge level detection circuits in the laptop. This will help in more accurately predicting the remaining charge level in the battery.