Converging aircraft means holes are lining up in the proverbial cheese. Two aircraft then making incorrect turns to increase rate of convergence is blowing a couple of huge new holes in the cheese.
Yeah yeah, 3 miles separation is great, but the 747 is still one of the fastest heavies and two of them swinging towards each other will gobble that distance up in no time, even if they're not approaching head-on.
Certainly would like to know reason for initial convergence path but much more disturbed by lack of insight into reason four experienced personnel on two flight decks were lulled into making a potentially catastrophic change of direction.