||CYA - you mistranslated your father.
He wrote: Ulam vadai bzman hazeh leit man d'palig shetzarich lechasot harosh kol hayom
You translated: Surely in this time noone argues that you need to cover your head all day"
But this turns the meaning upside down!!
What your father meant, I beleive is this:"
Today, __everyone agrees__ that you must cover your head at all times.
You tried to give a literal (instead of a figurative) translation, and in so doing you missused the verb "argues." In your (mis)translation, you are actually saying "Today no one would claim ie, put forth the argument. ie "argue") that you need to cover your head all day,' with the implication being that a kippa is not necessary!
Please straighten this out! you just told all your readers that a kippa is not needed!