Because if they did interact, directly, with the Higgs field, this would imply that neutrinos could have both chiralities; however only left-handed neutrinos and right-handed neutrinos have been experimentally observed.

Neutrinos could, in principle, interact with the Higgs field, directly, very weakly, consistent with the property that, as is now known, they do have mass; it suffices to ensure that the coupling is so weak that the right handed neutrinos are produced too rarely to be observed.

That's why there are experiments that are being done/planned to try and deduce, indirectly, whether neutrinos could obtain their mass by such an interaction: https://en.wikipedia.org/wiki/Neutrinoless_double_beta_decay#:~:text=The%20neutrinoless%20double%20beta%20decay,it%20has%20not%20been%20found.

The reason that photons don't interact, directly, with the Higgs field is different: It's because the Higgs field doesn't carry electric charge and the photons don't carry weak hypercharge.

However photons do interact with the Higgs indirectly and, indeed, it was by measuring this interaction, among other ways the Higgs interacts, that the Higgs particle was found.

Thanks and why photons do not react with Higgs field?

I mentioned it: They don'y interact directly, since the Higgs particle doesn't carry electric charge (and photons only interact directly with particles that carry electric charge); and, while the Higgs particle does carry weak hypercharge, the photon doesn't.

They do interact, indirectly, in a way that involves other particles, that carry both kinds of charges.

Ok sir thankyou.

Neutrinos and photons are the only elementary particles that don't interact with the Higgs field. The process by which neutrinos acquire mass is different. It's not known if neutrinos have a non-zero mass, it's believed they are massless.