Here's how I break down the last little bit there. The setup is UA 663 heavy in position on 28L, JB 1413 on final for 28L, and UA 1723 staggered behind them for 28R.
The controller realizes the spacing is tight between Jet Blue and UA663 on the runway, and asks JB1413 for the S-turn to slow them down a bit. However the spacing is still to tight, so JB1413 requests a late sidestep to 28R which tower approves. The problem is that this now puts UA1723 too close in trail behind JB1413 for 28R so 1723 is asked to sidestep to 28L, which the heavy will be clear of. UA1723 is unable to comply, likely (and this is a guess) because they are not allowed to make such a maneuver below a certain point on the approach. As a result tower has them go around, since JB 1413 will still be on the runway. Finally (and this is another guess, not really clear on the tapes), JB 1413 finds that the late sidestep isn't going to allow them enough time to get stabilized on 28R, and becomes the 3rd go around.
Just to Monday morning quarterback, she probably should have just sent JB 1413 around to begin with. At least that would have let UA 1723 get in.