I take it as him considering killing his father and his race as a personal slight. Similar to when Cell killed Trunks and Vegeta was angry that someone killed his son, not because he cared for Trunks, but because how dare someone kill his possession. Textbook narcissism.
He cried on Namek because it hurt his ego that Freeza used him, that he wasn't the strongest, that he wasn't going to fulfill his life ambition of being top dog and because of the above. Maybe as a child he was sad his father died due to actually loving him (we don't see his relationship with his father in detail though, so can't be sure), considering later on in life he was able to have genuine love for at least Bulma and Trunks and it seems like Saiyans can have genuine affection even without the experience of living of Earth (judging from Burdock and from Cabba), but I think on Namek it was almost entirely about his ego, if not entirely.