Spearman's rho correlation is considered non-parametric because it is the correlational test used when finding the association between two variables measured at an ordinal level. Ordinal level measurement does not possess a "true zero" and therefore cannot possess the precision and accuracy of continuous variables.
Pearson's r is used when correlating two continuous variables. However, one MUST check for the assumption of normality and identify and make decisions about any outliers (observations more than 3.29 standard deviations away from the mean). This is of PARAMOUNT IMPORTANCE because correlations are highly influenced by outlying observations. Just ONE outlier can artifically skew a correlation positively or negatively, and in a statistically significant fashion!
Going back to the introduction, remember to use Spearman's rho on interval and ordinal variables as well as with variables that are naturally skewed. Statistics, in and of itself as a science, is very flawed. Not everything you come across in existence will fit the normal curve. Luckily, we have non-parametric statistics that are robust to these common violations of inferential statistical tests.