  We revisit the Bogoliubov theory of quantum droplets proposed by Petrov
{[}Phys. Rev. Lett. \textbf{115}, 155302 (2015){]} for an ultracold Bose-Bose
mixture, where the mean-field collapse is stabilized by the Lee-Huang-Yang
quantum fluctuations. We show that a loophole in Petrov's theory, i.e., the
ignorance of the softening complex Bogoliubov spectrum, can be naturally
removed by the introduction of bosonic pairing. The pairing leads to weaker
mean-field attractions, and also stronger Lee-Huang-Yang term in the case of
unequal intraspecies interactions. As a result, the equilibrium density for the
formation of self-bound droplets significantly decrease in the deep droplet
regime, in agreement with a recent observation from diffusion Monte Carlo
simulations. Our construction of a consistent Bogoliubov theory paves the way
to understand the puzzling low critical number of small quantum droplets
observed in the experiment {[}Science \textbf{359}, 301 (2018){]}.
