in quantreg the err or distant in objective function is measured as abs(y--x*b) (L1 problem) while in usual regression the err is measured as (y--x*b)**2 (L2 problem).

So importance of each data point will depends the distance in L1 and distance^2 in L2.

So the estimates in L2 is much easier impacted by a 'bad'/away from average point than that in L1. But it has a close form solution and easy to deal with in math and in computation.

That is why quantreg is said as robust regression.