One way to look at this is the simple sequence of events, which begins with the father's thought that starts with a woman (the wife), then eventually comes entry into an excited phase, and finally, finalizes in - offspring!
Thus the son extended from his father's thoughts, from the early thoughts and through the entire sequence of thoughts that led to actions, which eventuated into childbirth.
This is the sense to make of Torah's use of "the son" as an analogy. (E.g., Ex. 4:22, Deut. 14:1) It all begins with a thought. In that sense, the Torah and the universe were created - to serve the first "thought" God originally had for the process - the Jewish People. God chose the Jewish People around which to create a world and around Torah.
Obviously the idea of God having a physical son is preposterous because God is not corporeal. But here, in Tanya, we see the clear connection to God from a spiritual sense, in that God's "ethereal" thoughts delivered a Jewish People. (You can't get any more ethereal than considering thought be the "act" of creation.)
But since in Torah itself the phrases so often spoken are "Speak to the Jewish People" or "Tell the Jewish People", it follows that Torah too subserves the original thought that led to the whole process - the Jewish People.
In this way the Jewish Nation is an "extension" of "his father's brain" - God!
(We spoke to the physical aspect of this phenomenon as well, where the semen has as its original locale, inside the developing embryo, cells from which the brain differentiates. In other words, the sperm the father released to create a child derived originally from where his brain began to develop and from there, during an early phase of embryonic development, migrated to the testes, where, from then on, these cells only undergo meiotic division and live for the rest of their lives as potential or actual sperm cells: LINK)