The restoration of the time-reversal symmetry in a system of ultrahigh energy cosmic neutrinos involving metaneutrinos is discussed. Cosmic neutrinos reaching the Earth’s surface correspond to cosmic metaneutrinos moving in the opposite direction. This can create the illusion of some radiation directed upward from the surface of the Earth. An alternative interpretation of the unusual upward-pointed cosmic-ray-like impulsive radio event recorded during Antarctic Impulsive Transient Antenna (ANITA) flights is proposed. Our approach take into account the interaction of ultra-high energy cosmic metaneutrinos with the Antarctic polar ice, which was detected in ANITA experiments by means of the Ackaryan emission.