Non-robustness of parametric statistics Why is parametric test considered to be non-robust ?
Or, why is parametric test not considered to be robust?
 A: 
Why is parametric test considered to be non-robust ? Or, why is parametric test not considered to be robust?

Strictly speaking, for this to apply you'd have to say which parametric tests and which kind of robustness you're looking at (robustness of what - level? power? -- and against what kind of departures from assumptions?)
As a generalization, it really isn't true; some parametric tests are quite robust.
Certainly some parametric tests really aren't robust - at least against some things.
The classic example is the F-test for normal variances, which is definitely not level-robust to deviations from normality.
But consider, for example, a two-sample parametric test for location in the logistic distribution (let's say we're dealing with a likelihood ratio test). It's pretty robust to departures from the parametric distributional assumptions; it can deal with lighter or heavier tails reasonably well - it's at least reasonably level-robust, especially against smooth, symmetric, equal-variance departures from the assumptions.
The t-test does fairly well for moderate departures from normality; however, it's not so (level-)robust to departures from equal variance unless sample sizes are equal or quite close to it. However the Welch test (which is still parametric) is reasonably robust against departures from equal variance and moderate departures from normality.
