Why would they have mass?
Theories where all particles are massless are much easier. So historically the question was the opposite: How can particles have mass? That question was especially tricky for particles that are responsible for interactions. In the 1960s, a couple of theorists found a way to give some of these particles mass: The Higgs mechanism. They predicted that there should be a new particle, too, the Higgs boson. If it exists (it was discovered in 2012) it would allow the W and Z bosons to have mass, but you still cannot give a mass to all particles. The photon has to stay massless.
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