Hell, Gohan called him out on it during their training session when he told his father to stop treating him as his son and fight him as a fellow warrior. Combined with feeling Gohan's potential to surpass Cell, he became stuck in a mindset where he saw his son as the perfect opponent to defeat Cell and treated him like any other martial artist, temporarily forgetting that he was still an inexperienced kid compared to everyone else.
And as for why he gave a Senzu Bean to Cell, that has less to do with Goku's acumen as a parent and more to do with it being that it's Goku. This is the same guy who let Piccolo get a free shot at him because Kami intervened, despite the fact that the former was established as a major threat to the world and allowed Vegeta to escape so that he could redeem his loss against him, even admitting that it was selfish of him. He tends to apply fair play and warrior ethics to situations where such a sentiment is not practical, but that's how his sense of morality works. Plus, Goku was thinking solely about Gohan's power level and prowess, and how they would negate make any Zenkai gains from Cell's recovery (and he was ultimately proven right, but I digress). And Super (and OVAs like Son Goku and Friends Returns!, which take place with the same timeframe) clearly shows us that he spends time with his family as much as he can while continuing his training.