Why do felsic materials have lower melting points than mafic?
Good question! As you know, Bowen's reaction series describes the order of crystallization of silicate minerals in a cooling magma. 

The complex anion of silicates is a tetrahedron of four oxygen atoms surrounding one silicon atom, connected with strong covalent bonds. Each tetrahedron may be isolated from one another or they may be bonded together covalently by sharing oxygen atoms between adjacent tetrahedra. In this way they may form single chains (pyroxene), double chains (amphibole), sheets (biotite), and three-dimensional networks of interlocking tetrahedra (quartz).

Each of these covalently bonded structural groups (except 3D networks) is bonded to its neighboring structural group (e.g. single chain to single chain) by ionic bonds with intervening cations (K+, Na+, Ca2+, Mg2+, Fe2+, etc.).

Relatively speaking, covalent bonds have lower melting points than ionic bonds. Source

In Bowen's reaction series, the minerals that form at the cooler end of the discontinuous series are richer in silicon and oxygen and poorer in metal cations. Therefore, the minerals at the cooler end are also more dominated by covalent bonds over ionic bonds. This prevalence is the reason why felsic minerals melt at lower temperatures than mafic ones.

Your logic is correct when looking at mineral stability in the face of chemical weathering. At the Earth's surface, those covalent bonds are much more stable and minerals like quartz tend to be much more resistant to weathering than olivine or pyroxene. This is described in the Goldich stability series, which I like to think of as Bowen's reaction series stood on its head.