Did Catholics invent fasting? For a good answer to that, read this primer.
Is fasting a useless exercise? No. Physical exercise briefly denies the body of rest and relaxation. Dietary restrictions deny the body of certain unhealthy foods -- usually the ones that are the most pleasant. Athletes and health-conscious people understand the importance of such self-denial. They also understand the importance of discipline, which is an excellent result of such self-denials. In the same way, the Church has always understood the importance of self-denial through fasting. It's strange, however, that while athletes and health buffs are lauded for their discipline, Catholics and Orthodox are sometimes derided for their fasting.
I know that one of the perceptions from the outside is that we fast because of a guilt-driven need to punish ourselves. Well, no, that would be insane and pointless. We fast because we need to master our appetites, to show our appetites who's boss -- our will. By our will we can then discern that those things which we craved, which we thought we needed, are not so necessary after all. By the same lights, we might realize that we're better off without them. To fast with the right attitude is to find out that we are more free than we thought we were.