Push a post off-centre and it is doing two things at once: carrying an axial load and resisting a moment. Both produce a normal stress on the same fibre, pointing the same way along the member's axis — so they simply add: $\sigma = \dfrac{P}{A} + \dfrac{Mc}{I}$. Read aloud: sigma equals P over A plus M c over I. $P$ is the axial force in newtons; $A$ the gross cross-sectional area in $\mathrm{mm^2}$; $M$ the bending moment at the section; $c$ the distance from the neutral axis to the fibre you are asking about — half the depth for the extreme fibre, never the whole depth; and $I$ the second moment of area about the bending axis, in $\mathrm{mm^4}$.

The plus sign does the teaching. On one face the bending pushes the same way as the axial load and the two add; on the opposite face the bending pushes back and the two subtract. One member, one load case, two different answers depending on which face you stand at — and the exam always wants both. In this lesson we count compression as positive, since the post is in compression to begin with; a NEGATIVE answer therefore means that fibre has gone into tension.

That negative answer is the whole reason engineers care. Concrete and masonry are hopeless in tension, so the design question becomes: how far off centre may the load sit before the far face is pulled? The region where it may sit safely is called the kern of the section, and for a rectangle it reaches one sixth of the depth either way. The middle-third rule your bricklayer quotes is exactly this arithmetic, worn smooth.