Tar becomes brittle when it loses softer fractions, oxidises, weathers, and can no longer move with the material beneath it.
Fresh tar is usually flexible because it contains oily and resinous parts. Over time, some of those parts evaporate, wash out, react with air, or become locked into a harder surface. The coating that remains can become less able to stretch.
Sunlight and heat speed this change at the surface. Rain, salt, and dust add physical wear. A tar coating on a shaded beam may age slowly, while the same material on a sun-exposed roof edge can harden, dull, and crack faster.
Brittleness is especially obvious where the underlying material moves. Wood swells and shrinks. Roof materials expand and contract. Rope bends. If the tar has lost flexibility, those movements open cracks. The coating may then flake away in hard pieces.
Brittle tar is often a sign of age, exposure, or a coating that has gone too long without renewal. It can still be historically interesting, but as protection it is weaker than a bonded, flexible, water-shedding surface.