When you have a big decision to make, you might have a couple of different ways to do it. Argument in the alternative means that you look at both of those different ways and decide which one is better. It's like when you are trying to decide whether to have an apple or a banana for a snack. You think about the good things about both the apple and the banana, and then you decide which one you want to eat. This is called argument in the alternative because you're presenting two alternatives (apple and banana) and then making an argument for the one you want to choose.