rub off on

"Talk like TED" からの引用です。
"You can give somebody an idea. If that person doesn't want to do it, what are you going to do? The passion that the person has for her own growth is the most important thing. And then we help them to go and find the knowledge, because nobody in the world can succeed alone. The person with the idea may not have the knowledge, but the knowledge is available." You are reading his because you have a passion for personal growth. You've probably mastered (or are close to mastering) the topic on which you speak. Don't be afraid to share your excitement. It will rub off on your audience.
"rub off" だとこすれ落ちる感じですが、その後に "on" があるので、こすれ落ちた後に "on" の後に引っ付くのでしょうか？　辞書を見ます。

・Oxford English Dictionary: Be transferred by contact or association.: When parents are having a hard time, their tension can easily rub off on the kids.

・Collins Dictionary: If someone's qualities or habits rub off on you, you develop some of their qualities or habits after spending time with them.: He was a tremendously enthusiastic teacher and that rubbed off on all the children.

・Cambridge English Dictionary: If a quality or characteristic that someone has rubs off, other people begin to have it because they have been with that person and learned it from them: His enthusiasm is starting to rub off on the rest of us.
なるほど、受け継げられる、影響を受けるのですね。