The following article contains spoilers from Future State: Gotham #14, on sale now.
Nightwing's behavior since his brain injection has been strange to say the least. He has gained precognitive abilities and seems aware of what's to come in the immediate future, but has been tightlipped about it, and acting with increasingly less emotion. At the time, it seemed to be a side effect of the drug, but Future State: Gotham #14 (by Dennis Culver, Giannis Milogiannis, Geoffo, Troy Peteri) hinted that there is a much more noble, and devastating, reason for Nightwing's recent choices.
In the issue, he confronted the Next Batman to try and make him stop being the Dark Knight. Thanks to his new powers, he won the fight handily, but told Jace that he has to stop being Batman if he wanted to continue living. While this seemed like a threat from Nightwing, there were other moments in this issue that implied something else is motivating his aggressive decision to be Gotham City's one and only Batman.
Now, Nightwing is a hero who very much values his family, friends, and community. In his normal state, more heroes would be something he would welcome. Yet, this issue made it very clear that he believes Gotham needs only one Batman, showing a sudden dissatisfaction with the current one, something that he hadn't expressed before. Adding to this, when Batgirl confronted him about what it was he had seen in the future, he looked as if he was about to tell her, but then fought the urge.
His expression was pained, there was no other way to describe. It looked as though Nightwing was physically hurt by having to hide something from someone he cares so much about. All of this, taken in conjunction with his warning to Jace to stop being Batman if he wanted to live, seems to suggest that Nightwing saw the various Batmen appearing in the future, and that one of them would die. This theory actually explains a lot of Nightwing's recent behavior, and why he refuses to share his foreknowledge of the danger to come.
Nightwing is an inherently selfless person. If his vision did show one of the Batmen dying, then it could have been any number of people he cared about, be it Damian, or Jace. This would have been an unacceptable loss for Nightwing, especially if that death was the price that had to be paid to save the world. To prevent this, he would have taken on the burden himself, trying to establish himself as Gotham's only Batman to ensure that he would be the one to sacrifice himself.
This would also explain his robotic behavior and refusal to share that knowledge with his allies. The cold-heartedness is just a front to make it easier to push them away. He is especially motivated to do so because he knows that if he told his family the truth, they would do everything in their power to stop him. Nightwing's belief in the accuracy of the vision is so absolute however that he could not let them do this.
It would bring unnecessary risk to them and potentially create an even worse future. Sacrificing himself, at least to him, would seem the more logical play here. He is the oldest, the first among them, if anyone was going to give it all up to save his family and world, it would be him.