What the symbol of the packet of meat suggests about Stanley Kowalski is that he's a primitive, savage man, almost like a caveman.

One can easily imagine Stanley, thousands of years ago, coming back home to his cave after a long hunt and unceremoniously depositing some fresh meat at his wife's feet. A much more modern, sophisticated man, on the other hand, could never be envisaged in such terms. Instead of throwing meat at his wife, he would've placed it on the kitchen counter as most normal people would.

Then again, there's nothing remotely sophisticated or modern about Stanley; he's a throwback to a time when men were expected to be forcefully and aggressively masculine. And Stella wouldn't want it any other way. She finds Stanley's machismo extremely attractive. Their powerful, carnal sexual relationship is symbolized by the pack of meat in that Stanley throws himself at Stella physically just like he hurls the pack of meat at her.