In general, minerals are most stable at the temperature and pressure at which they form. In the case of the igneous rock minerals described in Bowen's Reaction Series, the higher temperature minerals (such as olivine, pyroxene, etc.), when exposed at the surface, will be farthest from their comfort zone, and will therefore chemically weather at a faster rate.
Quartz, at the other end of Bowen's, is closer to its preferred temperature and should therefore be more stable (and it is). This is one reason why we find quartz sand at the beach, instead of olivine sand.
The weird thing that Bowen found concerned the discontinuous branch. At a certain temperature a magma might produce olivine, but if that same magma was allowed to cool further, the olivine would "react" with the residual magma, and change to the next mineral on the series (in this case pyroxene).
Continue cooling and the pyroxene would convert to amphibole, and then to biotite. Mighty strange stuff, but if you consider that most silicate minerals are made from slightly different proportions of the same 8 elements, all we're really doing here is adjusting the internal crystalline lattice to achieve stability at different temperatures. Really no big deal.
General Classification of Igneous Rocks
What Is the Difference Between Quartz and White Feldspar in Rocks?
What Is the Difference Between Phaneritic and Aphanitic Rocks?