I have another example to show the difference between "That's because..." and "That's why...":
Eg.: Mariah has no friends. That's because she's such an embittered person. (Mariah is an embittered person, so she has no friends, because she tends to keep people away from her.)
Mariah has no friends. That's why she's such an embittered person. (Mariah has become an embittered person because she's got no friends. She feels really bad about the fact of having no friends)
In the first example Mariah doesn't feel bad about having no friends. Well, maybe she does, but that feeling is not shown in the sentence. The fact of having no friends has to do with her being an embittered person, which's kind of offputting. On the other hand, in the second sentence, it justifies why Mariah is an embittered person, because she has no friends. This is the reason why she feels so bad. I hope to have made this blatantly clear.