Why does Apple use Objective-C?
Apple merged with NeXT in the '90s and Mac OS X was made from NeXT's operating system, NeXTSTEP. Objective-C was the official language of NeXTSTEP's application frameworks, which became Mac OS X's Cocoa. Mac OS X was then adapted into the iPhone OS, and Cocoa was made into Cocoa Touch. Objective-C has held up pretty well all along the way, and a lot of Cocoa's features would be difficult to translate into C++.
So essentially, it all comes from NeXT.
Objective C began life in 1983 I believe, created by Brad Cox and Tom Love. The idea of Objective-C was to take the purity and low-level control of C and merge that with true object-oriented features that would allow companies to customize system libraries that could communicate with the OOP layer of Obj-C. Essentially, it worked. Obj-C is a strict superset of C, unlike C++ which is most of C, but with many differences.
When Steve Jobs founded NeXT Computer (1985), he brought in some of his former Apple team and others. His best programmers were interested in using a language that expanded on C with the same speed benefits and system control. They chose Objective-C. NeXT eventually wrote many libraries and methods for the base language. These all begin with NS for Next Step. This was the name of the NeXT OS. By 1989 the Next Step OS was considered to be vastly superior to MS Windows or Mac OS, and many computer companies wanted to license it badly. Jobs simply didn't want to go in that direction.
Once Apple wised up and brought Steve Jobs back into the fold (1996), the infusion of Next Step OS into the new Mac OS X was really the key to Apple reviving its software and its programming strategy.
While C++ remains a truly excellent and powerful language, I find that Objective C has less flaws (just my opinion), and Apple's continued work on Cocoa libraries has made the Obj-C language a truly modern power with C underpinnings. Is it better than Java? Not sure. But for what it is primarily designed for (Mac OS, iOS) it is astonishingly good, if a bit overly verbose.
The greatest criticism of Obj-C is the syntactical styling, but any programmer that truly learns the language will quickly learn of its amazing power and seemless fit with all things Mac, iPhone, iPad.
Will any other platforms ultimately adopt Obj-C? not sure, but doubtful. But the Cocoa libraries are truly wonderful.