Title: Can we tell the planes'' truth? On the suggested origins of co-orbiting planes of satellite galaxies Abstract: Both major galaxies in the Local Group (LG) host planar distributions of co-orbiting satellite galaxies: the Vast Polar Structure (VPOS) of the Milky Way and the Great Plane of Andromeda (GPoA). Similar structures, often associated with streams, are present around more distant hosts and might even be ubiquitous in the universe. I will discuss suggested formation scenarios for the satellite planes and their shortcomings. Even though not predicted by the ΛCDM model of cosmology, several recent studies claim that the VPOS and GPoA are consistent with sub-halo based satellites. Unfortunately, these studies either have flaws in their model satellite selection, do not consider all observational constraints, or are internally inconsistent. Correcting the analyses changes their results dramatically: the observed satellite galaxy planes remain extremely rare in ΛCDM simulations. Motivated by the fact that both major galaxies in the LG host mutually aligned satellite planes, I suggest that the LG can provide additional clues. Being part of a LG analog does not increase the chances of host halos in ΛCDM simulations to contain a VPOS-like satellite planes. However, I find that the observed phase-space distribution of the non-satellite dwarfs in the LG is also highly structured and indicates additional tensions with cosmological expectations, in particular in the number of likely backsplash galaxies and their distribution.