There are two theories about why the Tu-144 entered that dive that broke it apart:
1)The pilot was instinctively trying to avoid a mid-air with the Mirage III fighter he saw at the last second which appeared above and in front of him, or
2) He stalled his engines in his sharp climb and was trying to windmill them back on again by putting the plane into a sharp dive.
What I can say is that the Tu-144 did go into a steep power climb to show off at the air show. That alone invited disaster from Theory 2 even if Theory 1 is what actually happened.
My pet theory, however, is that the pilot fell out of his chair. Soviet pilot's seats were notoriously flimsy and wobbly, often borrowed from home. As this photo of an actual Tu-144 cockpit testifies.