We do not learn the same things that they learned in Ancient Rome, because (1) things have advanced, rendering certain data irrelevant, and (2) we have new things to learn, such as computer science, how to drive a car, and how our government works (if they’re even teaching any of that anymore). Some things, like the Iliad and Odyssey, are still taught, but they aren’t given the same emphasis. Certain other things, such as farming, spinning wool and linen, and fighting with a gladius are now considered specialized knowledge, not taught regularly, but you can still learn them if you know where to look.
That said, the trajectory of modern technology rests uneasily on the back of cheap fossil fuels which won’t always be there. It also assumes that we are too prosperous to have everybody needing to farm, spin, and fight, which (if the climate shifts unreasonably and we can no longer pour petrochemical fertilizers) won’t always be true, either. We’ve moved up on Maslow’s Hierarchy and don’t learn pure survival skills anymore, but it would be very easy to imagine a future where this is no longer true.
I believe that how we currently live is a historical anomaly of sorts – a harnessing of temporary power that allowed us to get all uppity for a while. In other words, we might not teach future generations what we currently do – but that the skills taught in the ancient (and early modern) world will be more relevant.