The journey of DC Comics' Damian Wayne is one that is full of conflict and turmoil. Constantly battling with an inner darkness thanks to his equally dark upbringing, Damian has finally reached his breaking point and has determined to go down dark paths, distancing himself from his role as Robin as well as his father Batman. Much of this has to do with Batman's lack of emotional range to be as available as a father should be. While Batman himself has admitted his failings to his son, it seems as though it's too little too late. However, when Nightwing was partners with Robin, he served as more of a positive father figure than Bruce Wayne had ever been, especially in recent comics.
The son of Batman and Talia al Ghul, Damian Wayne had no choice but to grow up fast under the tutelage of his grandfather Ra's al Ghul and his League of Assassins. By the age of ten, Damian had already become one of the deadliest killers in the world, and the supposed new Heir to the Demon. Batman didn't even know of his son's existence until this point, but quickly took him in and trained him further to restrain his killer instincts and become the next Robin. However, after Batman's supposed death and the Battle For The Cowl storyline, Nightwing took Bruce's place as Batman, and Damian worked by his side as his Robin. Dick Grayson would prove critical in helping mold Damian's new life and role in Gotham, tempering all that he had learned with the League and reshaping those skills into being a force for justice and good, without the need for lethal tactics. Grayson also expressed plenty of love and positive discipline towards the young hero, just as a father would, and on a deeper level than Bruce ever had.
While Damian would still be prideful, snobbish, and arrogant, he's always had a kinship and special bond with Nightwing as a result. Recently, in the DC Rebirth era, Robin and Nightwing talked about the good old days during Grant Morrison's run on the new Dynamic Duo, and Nightwing even revealed that he had considered keeping Damian as his partner even after Bruce came back.
Despite Nightwing's fears that he wouldn't be able to handle the responsibility of caring for Damian like a "father," it becomes pretty evident that he probably would've done a better job than Bruce has, especially considering recent events like the death of Alfred, who was killed by Bane right in front of Damian. In Teen Titans Annual #2 it was confirmed that Batman was not there for his son, instead choosing to deal with his own grief and suffering, throwing himself into his work at Batman and leaving Robin by himself. This is what has lead to Damain seeking lethal justice on criminals. He wants someone to punish. If not for Batman and the Teen Titans, Damian would have definitely killed KGBeast, who was responsible for shooting Nightwing in the head and almost killing him. Still, Damian has now abandoned his role as Robin and has run away from his father in favor of taking down criminals however he so chooses, even by lethal means.
While Nightwing might have been worried about whether or not he could have handled caring for Robin, it's clear that he would've done miles better than Batman. Unfortunately, Batman had expressed very few moments of care and affection to his son, despite that fact that he does indeed love Damian. Batman cares and loves all of those within his Bat Family, he's just terrible at showing it. His availability is lacking, especially when it's needed most, as seen in recent issues. Hopefully Batman can become better and reach out to his son on a deeper level like he always should have. For now, fans of the Batman mythos can look back at the healthier relationship between Nightwing and Robin, and imagine what could have been had it continued.