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?
This is a great question. Here is my opinion. Let's review the definition of a statistic, it is "A statistic (singular) or sample statistic is a single measure of some attribute of a sample (e.g. its arithmetic mean value)". So, it means a statistic only depends on the data, not parameters.
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.
Hope this helps.