Eugene Volokh points out that “thee” and “thou” (and the corresponding verb forms such as “shalt”), while they sound formal to us because they’re associated with the Bible, are originally the informal or intimate versions of of the second person pronoun, used either with kin and close friends or from superior to inferior.
Eugene is right about that, but the analysis can actually be carried a step further back. Before “thee” (French “tu,” German “du”) was informal or intimate, it was singular, while “you” was plural.
At some point, addressing a singular interlocutor on the second person plural became the formal or honorific version. (The connection of plurality with honor is maintained in the royal “we.”) Over time, the honorific plural became the normal polite form of address, and the singular was reserved for intimates and inferiors.
That had the unfortunate effect of eliminating the distinction between the singular and plural forms of the second person. In the sentence “I’m coming to see you” it’s clear that there’s only one of me (else it would be “We’re coming…”) but unclear whether I’m coming to see you as an individual or a group of which you are one. (The Southern regional “you-all” filled in this gap neatly, but failed to achieve standard status.)
The Quaker “thee” and “thou” now sound archaic, but when they were first adopted the informal/intimate second-person forms were still in active use.
The Quaker objection to the formal “you” was, as I understand it, two-fold. First, like removing one’s hat in the presence of superiors, it reflected what George Fox and his followers thought an inappropriate distinction among the social ranks, tending to blur what seemed to them the obvious fact that we are all equally the Children of God. Second, because the polite “you” was originally a plural form, using it for a singular indivual seemed to the early Friends a departure from strict veracity, on which they placed a high value.
I hope, Friend Reader, that thou hast clearly grasped these subtle distinctions. If not, and thou wilt email me, I will attempt to clarify it for thee.