I wrestled throughout youth and in high school. As said above, wrestling will teach an athlete dedication and toughness. Unlike a team sport, it is only you and your opponent on the mat.
As for weight cutting, back in my days, we took the weight off incorrectly. Again, the plastic suits were the norm, along with hot whirlpools. The State of Iowa has installed rules around cutting weight now in an attempt to curb the drastic weight cutting. You can only loose a certain percentage of your body fat. No more of wrestlers running to their family doctor's to get a note saying that they can drop an additional weight class. There is also a structure descent plan that must be followed. A wrestlers is only allowed to lose 1 1/2 percent of their body weight every week. This is strictly followed and you can't wrestle at a weight unless you abide by that descent plan.
For those of you thinking that weight cutting is only a wrestler-thing, there are many athletes in our high schools, especially female athletes, that are battling weight "issues".
It was also mentioned above about skin diseases. Yes, that can be an issues, BUT it is also an issue that can be taken care of by a few cleaning steps. Wrestling mats have to cleaned on a regular basis. I know that our wrestling clubs cleans the mats before every practice. Wrestlers must also clean themselves when their practice/competition is completed. And you always have to look for signs of ring worm and others that are out there. When you go to other tournaments, you can't depend on the hosts to make sure that the mats are properly cleaned.