So I was studying special relativity and came across the twin paradox. When I searched for the explanation for it I saw that the person going on the spaceship accelerates with respect to earth and so the the direction of time is rotated, so the person on spaceship's clock moves slower and both of them would agree on it. When I asked doesn't the person on earth also accelerate with respect to the person on spaceship I was told that since they both accelerate relative to each other but only the person on spaceship has absolute acceleration.
In SR (special relativity) each of the two observers in relative motion measures the other observer's clock ticking slower. A basic principle of SR is that the laws of physics are the same in any inertial reference frame.
In the twin paradox, the twin leaving the earth changes reference frame in order to return to the earth, thus experiencing an acceleration in his/her rest frame. Instead the twin on the earth continues in his/her reference frame, that is no acceleration. The absolute acceleration is the acceleration measured in the observer rest frame (proper acceleration).
The central principle of relativity is that
The laws of physics are the same in all inertial reference frames.
An inertial reference frame is defined as one in (among other things) Newton's First Law holds: an object in motion tends to remain in motion unless acted upon by an outside force.
Based on this, it's easier to see why we can't expect the two observers to have the same results. The rocket observer is not in an inertial reference frame, since during the phase that they were firing their rockets, they would have seen objects accelerating relative to the rocket without any force acting on them. Imagine a pen floating in the middle of the cabin; when the rockets turn on, the astronauts on the rocket would see the pen mysteriously pushed towards the back of the rocket, in the absence of any force.
Absolute acceleration in the explanation you were given likely refers to a reference frame with respect to "the matter of the universe at large" described by French, A.P. (1968). Special Relativity. W.W. Norton, New York. p. 156.
"Note, though, that we are appealing to the reality of A's acceleration, and to the observability of the inertial forces associated with it. Would such effects as the twin paradox exist if the framework of fixed stars and distant galaxies were not there? Most physicists would say no. Our ultimate definition of an inertial frame may indeed be that it is a frame having zero acceleration with respect to the matter of the universe at large.")."