Why is furniture built with side panel grain being vertical?
The main original reason was purely a practical one, to more easily allow for wood movement. Wood expands/contracts largely across the grain (movement along its length is tiny and can safely be ignored in virtually all furniture work).
This vertical grain is now a convention and is followed when furniture has a veneered surface, e.g. in cabinets made from plywood1. I should say followed most of the time2.
When building in solid wood, to understand why this is important, just imagine if you had a chest of drawers which changed height through the seasons:
- At its 'widest' (tallest) the gaps between drawers would increase.
- At its 'narrowest' (shortest) it's possible the drawers would be so tightly squeezed they couldn't be opened, and there would be other problems.
The grain on the top panel is left to right.
The grain on tops was aligned to match that of the sides so that they expanded and contracted along the same axis.
When building in solid wood if a table, bureau, sideboard etc. had the grain oriented the other way the piece would change width through the seasons, causing havoc with any drawers or doors in their openings, plus literally scraping any feet across the floor (a surprising distance in wider pieces).
1 Historically this was important even in veneer work because the substrate was solid wood, e.g. pine boards, which needed to have their grain oriented vertically, not just to match the movement of the veneer on top but for the structural reasons outlined here.
2 As furniture is increasingly designed by people with no formal training or grounding in historical furniture, just made ad hoc by the maker with no specific design intention, or deliberately to look different or 'be modern' we can expect this convention to be increasingly eroded..... as a lot of furniture principles have been and continue to be in modern times.