The friction between two pages is quite weak. So how did friction grow to be so incredibly strong in this demonstration? 2 reasons:
When we interleave N pages on one side with N+1 pages on the other side, each side now experiences a total of 2N frictions.
Remember also that friction depends on how hard the two surfaces are pressed perpendicularly into each other. Consider the bottom page: it is now weighed down by 2N pages instead of just one. The next bottom-most page is weighed down by 2N-1 pages. And so on until the top page where the normal contact force is back to the weight of one single page.
So the total friction is multiplied by (1+2+…2N). The sum of this arithmetic progression is about 2N2.
It takes just over 30 pages on each side to amplify the friction by about 2000 times!