A successful totalitarian state cannot accommodate private loyalties, since private loyalties will often trump loyalty to the Party. Therefore, the Party in 1984 seeks to ensure that the only and ultimate loyalty its members have will be loyalty for the Party. They eliminate all potential private loyalties, such as the familial or the sexual.
If Winston and Julia owed private loyalties to each other, why did they ultimately betray each other? Does their betrayal mean that their love wasn't genuine to begin with?
Is it possible to feel so much loyalty towards a state that you include all of your fellow citizens in your "family?"
Chew on This
It is only by abolishing private loyalties altogether that the Party is able to ensure the undying loyalty of its constituents. This is its most powerful tool of control.
Winston and Julia are captured by the Thought Police at the height of their relationship - at the point when they professed their undying private loyalty to each other - because that constitutes the ultimate form of rebellion against the Party. This is why the Party doesn't apprehend them earlier.