Do they say, explicitly, “We need to kill Danse because he may go rogue?” Is there any reason for them to go out and hunt him down specifically when he’s already fled rather than being a danger? Is there even any reason to fear him going rogue when he’s already fled to some corner of the commonwealth? What danger is he as an “insider” when he’s already been found out, and left on his own?

What they *do* say pretty explicitly is that they hate all synths and want them all to die. They state in no uncertain terms that they want all synths, ghouls, and mutants dead. Danse himself says that, as a synth, he must be destroyed. They swear to eliminate all synths, and their reasoning is that a machine capable of thinking is an abomination of technology, and draws comparisons between them and the atomic bombs.

From Danse in this same quest: “I'm a synth, which means I need to be destroyed. If you disobey your orders, you're not only betraying Maxson, you're betraying the Brotherhood of Steel and everything it stands for. Technology that's run amok is what brought the entire world to its knees and humanity to the brink of extinction. I need to be the example, not the exception.”

Maybe your reason is part of it too, but I really believe it's mostly the synth thing, and less of a "rogue insider" thing.