TL;DR - As I understand it, the "bad" approach connects increasingly distant unvisited points to each other directly, wasting more solder in multiple arcs and eventually connecting the last point back to the 1st point '0'.
The "better" approach moves outward from the center 1 point at a time in either direction, so still back & forth, but only laying solder between directly neighboring points along the 'number line'.
The illustrations & explanations really aren't clear in a single static image. He doesn't explain what the dotted line means (is it soldered? Is it just motion? Seems inconsistent). Agree this is frustrating to encounter so early in what's supposed to be the "clear" algorithms book ...
Both the "closest neighbor" AND "closest pair" examples seem to "hopscotch" back & forth over point 0, which is the reason given for the 1st approach being bad. He even says the 2nd approach should also alternate left-right, so how is it any better? Because you only connect directly neighboring points to each other, building up the complete line incrementally.
The "bad" example (as I understand it):
1. 0 connects to 1
2. 1 jumps over 0 & connects to -1
3. -1 jumps over 0 & connects to 3
4. 3 jumps over 0 & connects to -5
5. -5 jumps over 0 & connects to 11
6. 11 jumps over 0 & connects to -21
7. -21 connects back to 0, completing the cycle.
These "hopscotch" back & forth over 0, but don't connect the points in a straight line. You wind up w/6 distinct 'lines' of soldered connections.
The "better" closest pair example:
1. 0 connects to 1.
2. 0 connects to -1
3. 1 connects to 3
4. -1 connects to -5
5. 3 connects to 11
6. -5 connects to -21
7. -21 connects to 11
8. Unstated, the robot arm apparently travels back to 0 afterward?
These also go back & forth over 0, but incrementally extend the existing straight line by one point at a time at each step. Instead of 6 arcs of solder, you have a single line for most of it, and then the 2nd connection of the outermost endpoints.