More Korbanot!

So as Carmit and I have been learning the wondrous details and fun facts behind the korban olah and korban minchah, Mrs. Perl has kindly advised us that we pay close attention to the ostensibly minor details behind the procedures because they actually matter. This seemed odd to me at first because if we're not using the korbanot today and they were only an ancient practice, why does it matter today that we know the seemingly trivial facts of each korban? Although each korban has distinctly different processes of actually bringing the korban, they seem so foreign to us today, and most of us probably find the process "nauseating" (in the words of Zahava). Therefore I pose the following question: Why on earth do the details matter?