Reminder 1: there are no right-handed neutrinos
Reminder 2: only left-handed fermions (and right-handed anti-fermions) participate in “weak nuclear” interactions. This violates P-symmetry which is the symmetry under parity transformation. Electromagnetic and strong nuclear forces do not differentiate left-handed and right-handed particles but the weak nuclear force does. Parity transformation changes helicity (changes neutrino into anti-neutrino). Neutrino and anti-neutrino behave differently under weak nuclear interactions. This is why neutrinos are said to violate P-symmetry.
Reminder 3: elementary particle facts
I came across a Q&A prepared by the University of Illinois at Urbana-Champaign Physics Department. We need more tutorials like this.
In the tutorial (link shown above) there is a discussion of photon-photon collisions. In the blogpost titled “On the photon frequency” I mention that photons do not interact with other photons, they pass through each other because photons do not have electric charge.
In the blogpost titled “On the photon-photon interaction“, I remind readers that in the presence of strong electric and magnetic fields energetic photons may result in electron/positron pairs (real or virtual). There are many other possibilities: virtual quarks or leptons (and the antiparticles associated with them) may be created as well. These entities interact (via electromagnetic force or via strong-nuclear force) and then transform into real photons again. The entire process would have the appearance of photon-photon scattering. This is an extremely rare process. Only few photons will interact in such a way.