The twin paradox may help. Before you say “No, that is asymmetrical!”, let me explain.

In the twin paradox one twin stays on earth while the other twin travels on a spaceship to a star and back. The twin who travels ages less than the twin who stayed on earth. Some then ask "But if we switch things around and consider that the twin on the spaceship was at rest and the earth and star did all the moving, don't we then find that the earth twin ages less?" And the answer is no, we don't. We get the exact same result. Whether the earth and star do the moving or the spaceship, the result is always that the twin on the spaceship ages less.

To best see what is happening, consider that the earth and star is a long rod, say 3 ly in length, and that the spaceship is traveling at 0.6c and traversing this rod from end to end.

Scenario 1: The ship is moving at 0.6c and passes the stationary rod. How long does it take the ship to traverse the rod? From both perspectives?

Scenario 2: The rod is moving at 0.6c and passes the stationary ship. How long does it take the ship to traverse the rod? From both perspectives?

Scenario 1 Result: From the rod's perspective the ship is going at 0.6c and the rod is 3 ly long and it takes 5 years. From the ship's perspective, the rod is 2.4 ly long (contracted) and the ship is going 0.6c and it takes 4 years.

Scenario 2 Result: From the ship's perspective, the rod is 2.4 ly long (contracted), the ship is going 0.6c, it takes 4 years. From the rod's perspective, the ship is going 0.6c and the rod is 3 ly long, it takes 5 years.

So you see, unlike what your hear, the twin paradox is quite symmetric in the sense that the principle of relativity applies (as it always should) and you can have the spaceship move or the earth and star move. Ok, now you say "But this is even worse! You showed symmetric scenarios but now the results are asymmetric!”

Well, the twin paradox is symmetric in the sense that it follows the principle of relativity, but there is an important detail, which distinguishes it from your scenario.

When two observers A & B pass each other at some velocity, we often say that A sees B's clock running slow and B sees A's clock running slow. And this is true. But what does "sees" mean? Well, one way to define it is like this. If A pulls out a ruler and times how long it takes B to traverse it, and B times this as well, A's time will be longer than B's time. Likewise, if B pulls out a ruler and times how long it takes A to traverse it, and A times this as well, B's time will be longer than A's time.

But each is using their own ruler and this represents two different scenarios that cannot be compared. Thus, no paradox (since you can’t compare the scenarios anyways). You can only compare the two results if they are based on one ruler.

In the twin paradox, we are only using one ruler (the rod) the whole time. Basically, the distance from the earth to the star. That ruler was ALWAYS in earth’s frame, even though we looked at it with the spaceship stationary and with the spaceship moving.

In your scenario, you have to settle on which way you are going to go. Are you going to use A’s ruler or B’s? Do you want A’s clock to be slower than B’s or the other way around.

Also, if you think through this some more, once you choose a ruler, the other observer sort of has to come back to that reference frame at some point for the different clocks to mean anything. Having the two observers go away from each other forever makes the case of clock differences moot.