Why didn't Caeser personally groom his biological son Caeserion to be next ruler of

[Lyfe]

Rome? Everybody knows that while Caesar was out with his many Roman legions he somehow ended up in Egypt and ended up seducing/ and or being seduced by Egypt's last Pharoah of the Ptlomeic dynasty. Now as I uderstand history, it states that Octavian was the adopted "Great Grand-Nephew" of Caesar. He (o Octavian then goes on to crush all political foes in and throughout Rome's Republic. Eventually defeating his former alley and Cleopatra's then lover Mark Antony at the naval battle of Antium. Now I know by watching various documentarys about Cleopatra and her ambitions for her son to one day rule Egypt and Rome as Pharoah. She believed Caeserion's birth right as the only biological son of the great Gaius Julius Caesar was for him to fulfill this destiny. But for some reason that has possibly been lost to history as to why Caesar didn't openly express any eagerness to put in any position of power in Rome. Now I know Octavian eventually had his Roman Legions brutally trackdown and murder the young Caeserion, some think so that when Octavian finally returned to Rome to claim the title of imperator (emperor) of Rome he would not be challenged by Caeser's biological "illigitamate?" son. I know Caeser had brought Cleopatra and the young Ceserion to Rome on several occasions, only to be scorned at by Roman senators and other romans who held high positions of power at the time. I don't think this question has an absolute right or wrong answer that can be set into stone unless we were able to ask the man who knew best why he handled his "little Caesar" problem the way that he did. All I would like is your opinion on the matter mixed with and/or backed up by some historic fact. The person who convinces me and sways me toward their theory the best will get the points. Good luck and thanks in advance for taking the time out to ponder this minor historical question that has possibly vexed many ancient Roman historians who thousands of years.