The arguments in the video are obviously not a panacea; but I would be interested in knowing what aspect of the argument you identified as logical fallacies or entailed through inculcation.
Regarding the position on hijab & its specific manifestations in the form of covering the head or covering th face.., I am not as learned to make any specific comment as to what constitutes the righteous position on this subject from a doctrinal or theological perspective , but from what I know regarding this subject; it is discussed in Hadith & the specific commandments/obligations on this topic follow from there, therefore only the Munkareen-e-Hadith challenge the obligatory status of Hijab , & all conventional theological schools within the ummah accept Hijab to be a religious obligation.