I think the intention though is that he avoid her, not get close to her, especially with the context that he was dying and he didn't want to expose Gwen to even the heartbreak of another person she loved dying. Also especially since he used to really disliked Spider-Man and wanted to arrest him, since he used to have that feeling it seems like he now was acknowledging Peter being Spider-Man was necessary/acceptable but only if he was willing to be really self-sacrificing with respect to romance with his daughter.
And even disliking Spider-Man he probably wouldn't think Peter would deliberately or recklessly endanger her in action so that also supports that he wanted a breakup so Peter wouldn't even inadvertently expose her danger.