In this letter, we report the results for the isovector polarized quark quasi-distribution functions ∆u(x, v) − ∆d(x, v) in the large Nc, calculated within the chiral quark-soliton model. It is shown that the polarized quark quasi-distributions present good convergence to the light-cone PDFs in the limit of the nucleon boost momentum PN → ∞ (or the velocity v → 1), compared to the case of the unpolarized isosinglet distributions.a This paper is dedicated to Maxim Vladimirovich ( †August, 2021), who was my teacher, collaborator and sincere friend.