The combination of baking powder and baking soda is necessary in dairy-free pumpkin bread because both ingredients play important roles in the leavening process. Baking powder releases carbon dioxide when exposed to moisture, which gives the bread a lift and makes it fluffy. Baking soda reacts with acids, like the buttermilk that might be used in a traditional pumpkin bread recipe. Since dairy-free recipes typically don't include buttermilk, you'd need to use baking powder and baking soda together to achieve the same results.  Using the two together also helps get a nice rise out of the bread since we aren't using yeast in this recipe.