Through out Genesis when the word begot is used it refers to one being the natural human parent of somebody ie Adam(ah) begot Cain and Abel.
I can not find any reason to believe that when the word begotten or begot is used it does not mean being the Father in a physical sense..
Let me suggest a reason then. When you read the term "begat" in Genesis, you are not reading the actual word used in Genesis, but an English translation of the original. If that term in the original was at that point in time referring to biological reproduction, and then the translator uses the term "begat" then it may appear that the term "begat" refers only to biological reproduction (though that does not rule out its use being a figurative referral). The question however is not whether the term begat does or does not refer to biological reproduction, but whether the term from which it is translated does or does not. And is that the term behind other places where the English term "begat" is also used. Answer, in the OT it does indeed refer to to one term,
yawlad, which means to bear, to cause, to give birth or to bring forth children. But in the new testament the original word that gets translated into English as "to beget" is most commonly (though not 100% of the time)
gennao which can and most generally does mean to procreate, but can also refer to any sort of generating or even regenerating activity.
Further, when one reads phrases like "only begotten", the term from whcih that particular phrase is translated is
mongenes and is uniquely used in the NT. In context we find that it is applied in reference not only to Jesus, but to Isaac as the monogenes of Abraham. Now, surely the author new that Isaac was not actually the only begotten son of Abraham, in fact not even the firstborn. But what Isaac was is the unique son who was the fulfillment of God's promise to Abraham to have a son via Sarah. So, despite the fact that you will find the term
monogenes translated as "only begotten" by many translators, I argue that it is not the best or even the properly connotated translation of that term.
One other thing I think we have to be careful of is proper understanding of the use and misuse of learning a words etemology. For instance, as I learned in a 3rd grade reading class today, the etemology of the English word "disaster" comes from Latin and Greek words meaning "star". One can see the connection when one recognizes that people once used to think that disasters were fortold in the stars. But, it would hardly follow that the use of the word today as anything whatsoever to do with stars.
Language changes with time, and the meaning and usage of the English word "begat" is one of those words in which we see this change. Those who insist that because a translator several centuries ago selected that term is what he thought was the best way to express a Hebrew or Greek thought in English, and today what people mean by the term is to procreate that it therefore follows that this is what the Hebrew and Greek writers were themselves expressing, are arguing backwards. It would be as if I was to look at the Qur'anic passage 4:144 "O ye who believe! Take not for friends unbelievers rather than believers: Do ye wish to offer Allah an open proof against yourselves? (Yusuf Ali) and interpret that to mean that the Qur'an says Muslims cannot be friends with non-Muslims because the English word used in the translation is friends. And then to substantiate myself I look at the Arabic and I find that indeed the Arabic word "Auliya' " does indeed translate as "friend." Would you not (have you not in other threads) dispute that interpretation as not being the best understanding of the passage, because you would respond the word that is translated "friend" can also be translated as "helper" or "protector", and you would argue that it is the last understanding that best carries the connotation of the original meaning behind the word translated as "friend."
So, too, I argue, despite the possibility of translating the idea contained in the original languages as beget, it does not convey the best connotation of its meaning if you make to exclusively refer to biological procreation.