Why acceleration is not relative in General Relativity?

I was thinking of it, If I say: "I'm moving at a velocity $v_1$ relative to a reference frame $M$ then the acceleration will be the derivative of $v_1$ relative to the reference frame $M$." In other words, from the perspective of my brother at home, I'm travelling at a velocity $v_1$ and I have an acceleration $a_1$. But from my perspective, he is travelling at $v_1$ (and I'm standing still) and thus his acceleration is $a_1$. But General Relativity tell us that acceleration is not relative, so why?