The hydrogen atom does not possess a net spin despite being composed of a proton and an electron, both of which have a spin of 1/2. This is because spin is an intrinsic property of subatomic particles, and when combined, their individual spins do not necessarily result in a net spin for the atom. The discussion highlights that the spin of hydrogen can effectively cancel out, depending on the alignment of the proton and electron spins. In contrast, deuterons, which consist of a proton and a neutron, can have a net spin due to the addition of the spins of their constituent quarks. Understanding the role of quarks and their spins is crucial in explaining the spin properties of nucleons.