Why do some meats get tougher with higher temperatures, while others become more tender?
This is a product of the cut more than of the animal. You're comparing shank with steak, which are two very different cuts.  In general, to get a tender cut with high temperature cooking you want a cut with lots of fat and connective tissue to render.  Leaner cuts will become dry and tough. 

The shank is a cut you could also get from a cow, so you could just as easily be working with beef (or veal) shank, in which case you would follow the same principle of higher temp = more tender.  This is due to the large amount of connective tissue (and fat, to a lesser extent) in the shank, as well as the fact that its a harder working part of the animal.  Cooking to a high temperature breaks down the connective tissue in the meat, leading to a moister, more tender finish.  

A steak, however, has less connective tissue, so overcooking it just makes it dry and tough.  You don't necessarily want it too rare though-- while for leaner steaks many people would say the rarer the better, for very heavily marbled and fatty cuts (like ribeyes) leaving them too rare fails to render the fat, which remains in tough, white streaks and interferes with the texture of the steak.  It should be noted that you could theoretically get a goat steak and the same principles that apply to beef would apply to it as well.