Look at the map you posted! It's missing the top and bottom of the map! How do you use this grid system in the North and South pole? YOU CAN'T!
...right. If you want to look at the North or South Pole, you use a different map. They're not even missing, they're just spread out somewhat more than in real life (but nowhere near as much as they would be on Mercator, which does have to be clipped at the poles). Just like if you want to navigate New York City, you use a map of NYC, and then you can use a different map if you want to navigate London. Maps don't have to show every bit of the world at once. I didn't think that was a difficult concept to understand.
Why would you show a Globe in Every school with Latitude and Longitude lines. But then when it comes to building a grid referencing system, you use something totally different?
They aren't different. If you zoom in enough on a globe, latitude and longitude lines make almost perfect squares. A grid of squares, one might say. That's what you're seeing on maps with square gridlines.
Seriously though, the only squares I see on that map are the ones nearest to the Equator!
Yes, because this map is a Robinson projection, not a Mercator projection. On a Mercator map, latitude and longitude lines make perfect squares. That makes it useful for navigators. It also makes it inaccurate around the poles. The Robinson projection preserves the sizes and shapes of landmasses better, at the cost of having curved longitude lines. You asked earlier why the gridlines aren't curved -- well, on this projection, they
are curved. And when they aren't curved, it's not because the world is flat, it's because the
projection is flat, and has certain properties.