Massless bosons but not massless fermions? I noticed some article on massless Weyl fermions and it got me thinking. I'm wondering if there is any explanation for why bosons (specifically gauge bosons) can be massless (photon and gluon) but we don't see any fundamental massless fermions (working from the most likely confirmed hypothesis that neutrinos are massive).
I know that the $W^\pm$ and $Z$ get mass from spontaneous symmetry breaking, so obviously not all gauge bosons are massless, but why do we see no fundamental massless fermions?
 A: The mechanism for "giving mass" to elementary bosons and fermions is different. 
With bosons, it is related to the gauge symmetry ($SU(3)_c \times SU(2)_L \times U(1)_Y$) which is partially broken (and become $SU(3)_c \times U(1)_{em})$. The unbroken part imposes its associated bosons (gluons and photon) to be massless to respect this symmetry. 
With fermions, there is no such constraint since their mass does not come from a gauge symmetry (with our current knowledge, fermions masses are put by hand via add hoc yukawa couplings). Therefore, the mass of the fermions is not predicted (contrary to the masses of bosons). So, asking "why do we see no fundamental massless fermions?", is equivalent as asking "why do we see fundamental fermions with their actual mass?". Answer: we don't know!
A: 
I'm wondering if there is any explanation for why bosons(specifically gauge bosons) can be massless (photon and gluon) but we don't see any fundamental massless fermions.

It's because a fermion is a "body", and because "the mass of a body is a measure of its energy content".  See Einstein's E=mc² paper. He talks about a body and an electron here. 
"The kinetic energy of the body with respect to ($\xi,\eta,\zeta$) diminishes as a result of the emission of light, and the amount of diminution is independent of the properties of the body. Moreover, the difference K0 − K1, like the kinetic energy of the electron (§ 10), depends on the velocity". 
IMHO it's clear he thought of the electron as a body, and of radiation (eg photons) as energy. So a photon is "not a body". It travels at the speed of light, it's never at rest, so it doesn't have a rest mass.   

I know that the W+/- and Z get mass from spontaneous symmetry breaking, so obviously not all gauge bosons are massless, but why do we see no fundamental massless fermions?

Because "elementary" fermions such as electrons and positrons aren't truly "fundamental". You can create them in gamma-gamma pair production. Each is akin to a 511keV photon in a gedanken mirror-box of its own making. In electron-positron annihilation you effectively open one box with another, whereupon each is a radiating body that loses mass. All of it. And then it's not there any more. Obviously there's a bit of a contradiction here between E=mc² and the Higgs mechanism, but that's one for another day.       
