The "I'm your cousin's cousin, so we're second cousins" explanation in this chapter is not at all how second cousins work.
First cousins are individuals who have the same set of grandparents, in other words the children of your aunt or uncle are your first cousins. Second cousins are individuals who have great-grandparents in common, in other words, your children and the children of your first cousins are second cousins to each other.