If we rephrase the twin paradox in such a way: George and Helen are twins. Helen is taking a rocket at a speed of 0.6c. When Helen flying passing the earth, they send each other a selfie, who are at the same age with smooth skins. Assume they will send each other a selfie again when Helen passes star A that is 3c away. Assume for each unit of their times, they will grow a wrinkle on their skin. So, after 5 units of time, George sends a selfie to Helen, and when Helen passes star A, Helen also sends a selfie to George. According to Special Relativity, it takes 4 units of Helen's time to reach star A, George received Helen's selfie with 4 wrinkles on her skin, no surprises here. Since George is leaving Helen at a speed of 0.6c relatively, Helen sees George's time ticked 3.2 units when she reaches star A. But when she received George's selfie with 5 wrinkles, instead of 3.2 wrinkles, she is surprised. What is wrong? Can you explain?
You are forgetting about the relativity of simultaneity.
To make the arrangement you have described symmetrical, imagine that Helen has a twin sister, Grace, who is following her 3 light years behind, and George has a twin brother Greg on the star three light years ahead.
Now, when Helen and George pass each other, they both have the same age and no wrinkles.
Fast forward to Helen arriving at the star- she has four wrinkles and meets Greg who has five wrinkles. Three light years away, Grace has arrived at the Earth and met George- Grace will have five wrinkles and George will have four. You will see that both Helen and George seem to have aged the same amount and to have aged less than Grace and Greg.
The reason why it seemed unsymmetrical in your description is that Helen and Greg overlooked the relativity of simultaneity. George took his selfie at a time that was simultaneous to Helen arriving at the star in his reference frame. In Helen's reference frame, however, George took his selfie at the wrong time- he should have taken it a year earlier to be simultaneous in her reference frame, so he should have taken a selfie showing himself with four wrinkles.
When Helen reaches the star, in her reference frame George's time has not reached 5 units yet. From the point of view of Helen, George's picture is sent some time after she arrived, and thus she should not be surprised. The confusion with this thought experiment is that you cannot define two events separated in space that are simultaneous for both, George and Helen. Thus they cannot send each other a picture simultaneously, unless you define simultaneous in what reference frame.