As said before, no one is telling people to make begging their main income. But to get the initial riding + starting skills its ok to do it, and its is by far the fastest way. And its pretty much 100% reliable.
Once you have lvl 20 riding and have enough gold to buy the skills your spec needs to level just looting mobs and selling cloth on the AH pays for everything, skills, outland and northrend riding. Picking up a profession for gold is great for leveling, but its not really that fast if you are just trying to get your first 10 gold, it just takes quite long.
Hence, the fastest way to get gold as a new player is to go into your major city and ask polite for a tiny amount to get you started. Thats a fact.