Odysseus's fixation upon his son could possibly be explained by the timeline.
A small thing that needs to be said is that according to Homer Odysseus left Telemachus a "newborn" (or at least so Menelaus says in the Odyssey). Interestingly is hard to tell how long Odysseus and Penelope have been married before they had Telemachus because the time line is not cut and clear.
It seems like their marriage took place during the oath of Tyndareus period when Odysseus was at Sparta as a suitor to Helen. From the Oath till Helen's infidelity or abduction or forced seduction by Aphrodite we see there were around 10 years of difference (quite frankly according to some accounts Helen mentions she was 20 years in Troy). That means that he and Penelope were potentially married at least a decade (which makes sense given that he made a wedding bed for her from scratch making it seem that their palace was also being rebuilt at that time)
But if Telemachus was newborn or almost newborn (like let's say about 1 year old tops) that means that Odysseus and Penelope were childless for almost a decade. Either that means they were having some issues aka Odysseus running errands in the kingdom or that they were trying very hard to have children and somehow they couldn't
Do you imagine what this means?
Odysseus potentially had to leave behind a son he wished for for almost a decade full and not to mention that Palamedes nearly killed him, that very son that he potentially tried so hard for and wished for so much!
Hell no wonder he names himself "Father of Telemachus" and quite frankly one can understand why he would hold a grudge against Palamedes (be it Higenius you follow where he frames him or be it Pausanias who says he drowned him) one can imagine why his brain would snap like that! If this hypothesis is correct that is.
