Backing off of micro-crack fracture theory, what your engineering introduction book is trying to hint at is the implications of Mohr's circle. To illustrate, from Wikipedia:
As you can see, when you have a stress in x-direction, a stress in y-direction, and a shear stress, you can convert the stress to a new arbitrary axis (x' and y') with a different normal and shear stress. Basic statics can resolve these forces:
$$\sigma_n = \frac{1}{2} ( \sigma_x + \sigma_y ) + \frac{1}{2} ( \sigma_x - \sigma_y )\cos 2\theta + \tau_{xy} \sin 2\theta$$
$$\tau_n = -\frac{1}{2}(\sigma_x - \sigma_y )\sin 2\theta + \tau_{xy}\cos 2\theta$$
In the case of a shaft under pure torsion, the equations simplify:
$$\sigma_n = \tau_{xy} \sin 2\theta$$
$$\tau_n = \tau_{xy}\cos 2\theta$$
If the primary failure method is shear failure, such as the case for most ductile materials, then this occurs when we look at the axis where $\theta = 0$, and the stress is entirely in shear. However, if we look at the axis where $\theta = 45$°, then the stress is all in tension normal stress. In this case, when the material fails easily in tension, it will fail in this direction.
The real world is actually more complicated with micro-crack fracture theory, stoichastic methods, and fatigue stress. However, when running designs, this is practice to keep in mind - just because the shear stress is low doesn't mean that the brittle material can handle the tensile forces. As the introduction to machine design book, this is simply to make you aware of this phenomenon and know there should be a difference. However, to handle this in the real world, design criteria methods such as Mohr-Coulomb Theory would be utilized for brittle materials, while von Mises yield criteria are used on ductile materials. Creep is used in plastics. A nice summary of other methods is listed at Colorado State.
