Well i dont exactly have an answer for that, but from what I understand, the lights doesn't really need to 'MUST' pass through F, it just happens that they do. For example for a perfectly manufactured lens or mirror, light rays will converge/diverge at point F or C.
For mirror that is not perfectly spherical or manufactured poorly (which means the lens have bumps or cracks on them, all the light rays will not pass through F or C. Some will, but those that are reflected/ diffracted from the defects, will converge elsewhere (not F or C)
Which is why if you are aware of a sight condition called astigmatism, this is formed due to awkwardly shaped eyelens. so the eye ended up having multiple F and C points. hence, causing blurry vision.
hope this helps ;)