Why did Sophie choose her son?
The basis of the question goes to to the heart of the choice Sophie has to make. There is little, if any, rational justification behind why she chooses what she chooses. This is probably the terrifying aspect behind both her choice and the Holocaust, in general. The absence of rationality and predictability is the true terror of the Holocaust. Millions of people were "chosen" to die, like Sophie's daughter. There was little in the way of rational justification behind that. There was nothing they did, nothing that was warranted behind this. The evil that was brought about through irrationality is what was so terrifying behind the Holocaust. At the same time, the survivors of the ordeal had little to go on in terms of why they lived. What was the differentiation between them and the person next to them who was sentenced to die at the hands of an SS Officer or in the gas chamber? What did one person do to live while another dies? The randomness of this, the arbitrary nature which ended up governing the laws of life and death during the Holocaust are played out in Sophie's choosing of her son to live and her daughter to die. The painful, agonizing, and yet random nature of this choice, where a mother must say, "Take my little girl," to the SS officer who is trying to pry both children away is the sum total of both Sophie's experience and, metaphorically speaking, the reality of so many who lived through the Holocaust. It is in this point where Sophie's narrative resonates quite lucidly.
Most likely she thought her son had a better chance of survival. The girl was too little and her son was, I believe, 11. The son was also her firstborn. And he was a boy.
Many people have complicated answers but I think she was just being practical in a horrific situation.