[nkoren]

In 3D characters animation, everything needs to be decomposed into "quads". Polygonal faces with more than 4 sides start behaving really weirdly under deformation -- there's more than one solution for how the resulting surface should be shaped -- whereas "quads" behave in a totally predictable fashion. I suspect that similar issues are at play here. You want the skin to be part of a deformable surface, and you want to minimize stresses during deformation. Hence: use quads.

[Doxin]

Except in 3d animation you use almost exclusively triangles when actually rendering anything. A quad can be subdivided in two ways to form two triangles leading to unpredictable behaviour.

That said, during modelling you almost exclusively create quads since those lend themselves well to editing with edge loops. The render engine then converts those to (unambiguous) triangles.

[nkoren]

That's true, but typically, quad-based models are not decomposed directly into triangles, but, rather, subdivision surfaces that do have a predictable resolution. In other words, a direct triangulation of a non-planar quad can be resolved in two contradictory ways -- but smoothing it out produces a hyperbolic paraboloid with just one consistent resolution.

[Doxin]

That's only true for subdivision surface modelling which isn't the most common way to do it at any rate.