Sufficient statistics not depending on the parameter

A statistics $$T(X)$$ is sufficient statistics for $$\theta$$ if the conditional distribution of the sample $$X$$ given the value of $$T(X)$$ does not depend on $$\theta$$.

( this is the definition of sufficient statistics from casella and berger statistical inference)

My question is why should the conditional distribution of sample given statistic $$T(X)$$ not depend on $$\theta$$ in order for $$T(X)$$ to be sufficient?

Sufficient statistics help statisticians to remove all the information of $$\theta$$ from the data. Personally, I always think this removal process as replacing process. Since we have $$T(X)$$, it is sufficient enough that we no longer need $$\theta$$ anymore.