WE are Private Ryan: the movie's impact is its symbolism.

Rating: Null/10 (28 December 1999)

It is important to see the act of "saving Private Ryan" as symbolic of WWII soldier's sacrifices made to give us the lives we now have. Sacrifices they made even when they couldn't see their part in the larger picture. This is why the film is bookended with the old man and his family: we see the results of the sacrifice of Miller's squad, results they couldn't see as their friends are being picked-off around them.
WE are Private Ryan, our way of life was saved by soldiers who fought and died for a cause beyond themselves, even when they couldn't always see the logic in it.
The ferocity of the battle scenes are necessary for the audience to begin to appreciate the horror that real men endured so that we could have the life we now enjoy.
The soldiers of WWII fought, even when it was hard, to give us the lives we now have. Now it is our responsibility, even when it is hard, to make something worthwhile out of the life they died for.
This is the point of "Saving Private Ryan".