Each variable is standardized to mean = 0, standard deviation =1. If you reject this as arbitrary, you are rejecting correlation analysis as a whole - this is exactly the same standardization done to two variables in bivariate correlation, extended to a multivariate data set.
PCA is a form of (or at least related to) correlation. With standardization the resulting transformation hihlights variables in the original data that are most highly correlated. Without standardization you're visualizing covariation. Unlike correlation, covariation is influenced by the magnitude of the variables.
By standardizing, you control for differences in the magnitude of the variables, and focus on their inherent variation instead.
PCA is a form of (or at least related to) correlation. With standardization the resulting transformation hihlights variables in the original data that are most highly correlated. Without standardization you're visualizing covariation. Unlike correlation, covariation is influenced by the magnitude of the variables.
By standardizing, you control for differences in the magnitude of the variables, and focus on their inherent variation instead.