You can travel in north-south direction to go around the world... but you can also travel east-west. Going around the equator halfway will see no north-south change, but still be halfway around the world... so that should make clear that two antipodal points can be much less than north-south change than between the North Pole to the South Pole. They can even manage to be the same latitude.
The Pacific Ocean point on your first map image can't be the right one if you look at a globe more. Or perhaps it can help to consider thean analogy of digging into a hill to kind of reflect upon the rough idea that the Earth is curved3-D\curved... if you were to dig in at Monterrey and came out at the same longitude in the Pacific, it'd be quite akin to digging into your hill towards the center... and coming out on the same side you started on. If you're going through the center, you need to come out on the opposite side, and looking at a globe, Monterrey and your SH Pacific point aren't really doing that. Sort of like these crude diagrams:
Likewise with digging through the Earth... there's a latitudinal component north(north-south,) and a longitudinal component (east-west) to all surface motion, and the ≈ 13,000 mile trip to . getget to the other side of the Earth will be some sort of combination of the two. The North pole to south pole trip is the extreme case where all motion is latitudinal north-south. The equator trip is the extreme case where all motion is longitudinal east-west. All other cases will require some of each, in the right proportions to crossaim the line between them through the center. Not unlike trying to cross from one side of a flat circular wall clock to the other. On it, you must be on the "opposite side" of the center both "up-down" and "left-right" to have passed through that center. So is the concept on the globe.
