Why do we use +1 and -1 for marginal decision boundaries in SVM
It's important for the optimization formulation of the SVM that $y_i=\{-1,1\}$ which is why it makes sense to also output $y=\{-1,1\}$. If we look at the soft-margin linear SVM we want to minimize:

$\left[\frac{1}{n}\sum_{i=1}^n\max{(0,1-y_i(w\cdot x_i+b))}\right]+\lambda\| w\| ^2$

The $y_i$ is either +1 or -1 which flips the hyperplane in the soft-margin definition of the problem.