It was shown that Etherington’s identity is paralogism. Etherington’s identity is based on the imaginary relativistic dilation of intrinsic time of the galaxy by (1+z) times, but the presence of a relativistic anisotropy of luminosity of stars quickly moving away from it is ignored in the frame of reference of spatial coordinates and time (FR) of the observer. Etherington did not take into account the fact that the Universe is homogeneous only in the comoving FR in the expanding Universe, and recklessly made a "mix" of the phenomena and features inherent in two different FRs. It is shown that, according to General Relativity (GR), only the transverse metric distances — the transverse comoving distance and the angular diameter distance similar to it — can obey the Hubble linear dependence. The transverse comoving distance belongs to the comoving FR in the ex-panding Universe and is determined by the redshift z of the emission wavelength. The angular diameter distance belongs to the FR of observer of an expanding Universe and is deter-mined by the redshift of the frequency of the emission wave. The luminosity distance is not the transverse metric distance and therefore its dependence on redshift is nonlinear. It is taken into account that the Hubble constant, like the length standards and the constant of the velocity of light, is a fun-damentally unchangeable quantity in the rigid FRs. Its exact value is empirically found.