Hi Jil, Welcome to English Forums. Thanks for joining us.
"So what?" is almost always intended as a rude, confrontational remark. "Hey, you just spilled hot coffee on my dress!" (reply) "So what?" (What if I did? What are you gonna do about it?)
"That's why" is sometimes intended as a rude remark. "Why are you so mean to me?" (reply) "Because you're ugly, that's
Only this is correct: I could not call you; that's why I sent an email. The 2nd would be correct if you changed it to this: I could not call you, so I sent an email. .