So this thing doesn't seem to go away. The Twin Paradox is a common question that gets asked in class and online. And of course, the most common answer being given to explain away the paradox is that there is a broken symmetry between the two twins, and thus, they should not experience the same thing. But often, this involves one twin experiencing an acceleration/deceleration, which the other twin did not experience.
However, in this video, Don Lincoln tries to correct the explanation and argues that even without any acceleration/deceleration, one twin will STILL not have the same set of experience (he/she is in two different reference frame, while the "non-moving" twin stays in just one reference frame) when compared to the other twin, and thus, this broken symmetry resolves the twin paradox.
The math is simple algebra, but you do have to keep the notation straight, and the signs.