As someone who is just starting to learn Java and ObjC, am I going down the wrong path? I'm sure this guy is exaggerating to a degree, but I'm not sure how much.
If you want to write mobile apps, you're pretty much stuck writing in those languages or using a framework that does the cross-platform shenanigans for you. Or writing web apps exclusively that have mobile browser support.
Regardless, neither Java nor Obj-C is going away anytime soon, so it would not be a mistake to learn either or both.