What is the difference between the sentence starting with "that's why ~" or "that's what ~" and the sentence starting with "that ~" like here?
Unfortunately, "that's why" and "that's what" cannot be used here because these phrases do not fit the context of this sentence. Instead of "that" here, you could say "the fact that". "That's why" is used to introduce a reason for something. "That's what" is used to introduce what something is, either a situation, physical object, or your thoughts. Ex: The fact that you can run fast is impressive. Ex: I'm visiting my parents this weekend. That's why I can't hang out. Ex: A: Do you want to drive to the beach? B: That's what I was thinking!