Yes it might not be so obvious form the headings, but the idea is that the first “cleave in two” might not really cutting along the right “plane”, and then we move things across the boundary after.
“cleaving” is a fun dramatic word, but it’s kinda the wrong metaphor, come to think of it. Really, it’s more like pulling two sides a part, and letting it rip “just happen” wherever the bonds are weakest. “Rip base in two” would be better, as paper rips are expected to by messy and not necessarily along the path desired a priori.