I'll elaborate on why the thesis and argument are the most important parts of the speech.
You could be talking on any topic, from a sentence your friend just said to an excerpt from shakespeare, and give an impromptu speech. Why give an impromptu speech, why analyze your topic at all, if you're not going to give your personal interpretation. And don't tell me you're just analyzing it from society's perspective, it's about YOU and how you feel about the topic. Your thesis is the summation of your feelings on the entire topic. It's your chance to say 'Here's what x means.' Your argument is your defense of your feelings on the topic.
The thesis and argument are the most important parts of your impromptu speech because they are the reason for the speech. They're why you want to talk about the topic and why what you think is true makes sense. Even if you're just talking about the topic because you're doing College Forensics and needed another event, you're doing college forensics! So you're giving an impromptu speech because you care enough to do forensics! Make it count!
That's what the thesis and argument are all about: making your speech important. Here's where you say 'This is the topic. I agree, because of this.' Or disagree or whatever. The entire point of the speech is not to give good examples, or to have perfect structure. It's just getting your point across, period.
That's why I like impromptu so much. It's all about YOU, your interpretation, and your ability to defend it. Your argument is a summary of your entire belief system with regards to the topic, your examples are just case studies of times when you've recognized your feelings elsewhere. What matters is what you think, and how you say it. That's what verbal communication is all about, and impromptu is verbal communication at its finest.
The Thesis and Argument is why you're talking about the topic at all. Without a good, clear thesis and a solid argument there is no reason to give a speech, period. So your thesis and argument should be the focus of your work on impromptu speaking and the entire point of why you've decided to speak up.
Later today I'll go on to cover the second most important part of Impromptu speaking, the main example.