What type of symmetry specifies in presence of what each not-charged particle (for example, neutrino) should have an antiparticle?

Question

I think that charging symmetry assumes antiparticle presence, which has an opposite charge sign . And what symmetry assumes existence of an antiparticle at a neutral particle

Answer 1

Anti-matter is not just the opposite charge sign. To convert matter to anti-matter you apply the C-parity operation which change more quantum numbers than just charge. In the case of the neutrino the lepton number is switched,