There are three reasons people tend to recommend ASIO drivers:
1) It is in nearly every case a guaranteed bit perfect delivery. No resampling or anything like that. That is not guaranteed to the same extent in other driver models necessarily
2) Many pro cards have good ASIO drivers and bad WDM drivers. They focus on ASIO since that's what most pro software likes and the WDM drivers are an afterthought. So you get things like MOTU interfaces that can only do one stereo pair via WDM, but all I/O via ASIO.
3) Because that's what most pro software uses so they just assume that's what you have to use. The "that's what we've always used because that's what we've always used," thing.
However that doesn't mean that YOUR card has better ASIO drivers. If it doesn't WASAPI or WDM/KS may well be a better option. For a really well designed card, like a RME, it won't matter what you choose all drivers are equally good and it'll work flawlessly in either mode. For a lot of cards, there is one that works better than the other, and for many consumer cards, ASIO just isn't an option.
They are just different ways of talking to the card, so you use the one that is right.