The key words are "in classical mechanics." Nobody wondered whether the mass of two stacked bricks was equal to the sum of the masses of the individual bricks. On the other hand, burning cloth seems to "leave behind" a lot less than you started with. Lavoisier's contribution was to demonstrate that even in chemical reactions, with shocking changes in color, state of matter, etc, mass was conserved.

Wilczek is discussing the ingrained assumption about the bricks.