Actually it was because the White Witch used magical food to get people addicted so she could control them. Edmund was forced to return to her and betray his family because he was manipulated and under her power.
I agree with the picture. The other explanation as Lucy being a Gryffindor, Susan a Slytherin, Edmund a Ravenclaw, and Peter a Hufflepuff I see the point but I feel like the original picture here is perfectly assigned.
The Chronicles of Narnia: The Lion, the Witch and the Wardrobe (2005)