This is quoted from Dr. Seuss, a kind of kooky writer, who displays examples of this quote throughout his works. Dr. Seuss shows this is his different children's books, that the only people who matter are the people who care enough to read his works.
I think that this quote is striking because I agree with it. The only people who should care about what you say are the people that really of are importance in your life, and those people who care about you don't mind if you say exactly how you are feeling. Yet those people who put down your thoughts or simply do not care, thus they do not matter and are a complete waste of valuable time!