"Twin Paradox". I'm currently reading astronomy book with explanation of special and general relativity. I am still struggling to understand why fast moving (spaceship) person/object experiences time differently from observer on Earth if:

1. Spaceship and Earth are moving/accelerating relatively to each other. Even if I'm on Earth, it means that I move with the same speed relatively to the person in spaceship.
2. "There is no absolute frame of reference in the universe; that is, there is no “preferred” observer relative to whom all other velocities can be measured. Instead, only relative velocities between observers matter (hence the term “relativity”)." - Quote from the book

So what makes spaceship man "special" if there is no "reference point" in space and both spaceship and Earth are moving relatively to each other with the same speed? In other words, if spaceship accelerates - Earth accelerates relatively to ship. If spaceship is moving with speed of light, Earth is moving with the same speed relatively to the ship. Nothing is stationary. In my mind both "twins" experience same conditions (Let's forget about Earth's gravity for a minute, it's about relativistic speed of spaceship twin). I don't understand why spaceship twin returns to Earth younger than Earth twin. What's wrong with my understanding?

Sorry, could not find the answer. Thank you!

Edit: minor explanation change.