Context. X-ray selected samples are known to miss galaxy clusters that are gas poor and have a low surface brightness. This is different for the optically selected samples such as the X-ray Unbiased Selected Sample (XUCS). Aims. We characterise the origin of galaxy clusters that are gas poor and have a low surface-brightness by studying covariances between various cluster properties at fixed mass using hydrodynamic cosmological simulations. Methods. We extracted ≈1800 galaxy clusters from a high-resolution Magneticum hydrodynamic cosmological simulation and computed covariances at fixed mass of the following properties: core-excised X-ray luminosity, gas fraction, hot gas temperature, formation redshift, matter density profile concentration, galaxy richness, fossilness parameter, and stellar mass of the bright central galaxy. We also compared the correlation between concentration and gas fractions in non-radiative simulations, and we followed the trajectories of particles inside galaxy clusters to assess the role of AGN depletion on the gas fraction. Results. In simulations and in observational data, differences in surface brightness are related to differences in gas fraction. Simulations show that the gas fraction strongly correlates with assembly time, in the sense that older clusters are gas poor. Clusters that formed earlier have lower gas fractions because the feedback of the active galactic nucleus ejected a significant amount of gas from the halo. When the X-ray luminosity is corrected for the gas fraction, it shows little or no covariance with other quantities. Conclusions. Older galaxy clusters tend to be gas poor and possess a low X-ray surface brightness because the feedback mechanism removes a significant fraction of gas from these objects. Moreover, we found that most of the LX covariance with the other quantities is explained by differences in the gas fraction.