There's a lot of fun in math. Do we really have to teach such dead material? If we could get a cadre of people who love math and who get it the way you get it or the way I get it -- people who know what math is about -- you don't need to tell them how to teach. You just leave them alone, and it'll be OK.1. Teaching is hard. You do need to teach them how to teach. It won't be OK.
2. His idea is that the main obstacle to excited students is the content, but kids encounter content through pedagogy. Content is not enough, and for that reason content-knowledgeable people is not enough.
Update: Patrick Honner clarifies Strogatz's position in the comments:
Maybe it's not clear from the context, but the "you just leave them alone, and it'll be ok" line refers to the administrative and curricular micromanaging that many teachers face nowadays. It isn't a claim that content-knowledgeable people are automatically good teachers.
In particular, Strogatz was talking about the freedom his Calculus teacher, Mr. Jofffray (the subject of The Calculus of Friendship) had in the way he taught the subject. The school trusted him. He could "put his own stamp" on the course--that is, teach it the way it made sense to him, and make his own personal pedagogic decisions.
It's also worth noting that, in the book, Strogatz points out that Mr. Joffray was not the most knowledgeable mathematician, even at the school where he taught. As a student, Strogatz was initially skeptical, but learned that a lot more than content went into making a great teacher.