The training that the cast (other than Matt Damon) were put through wasn't just physically tough, it was mentally tough, too. Spielberg wanted every soldier who appeared on screen to be able to understand the mindset of a World War II soldier, and so they had to be treated as such. That meant the real soldiers who were brought in to perform the training were exceptionally tough on them.
All of the cast were only allowed to refer to each other by their character's names. Their real names were left at the door. The trainers didn't even use their character names; they simply referred to each and every one of them, from Tom Hanks down to the smallest bit-part, as 'turds'. Soldiers on the front line in World War II certainly didn't feel special or unique, and so the cast had to know exactly how that felt.