Unbiasedness is not obviously desirable, which is the point worth making in an interview.
A biased estimator with much lower variance often has smaller mean squared error, and MSE = bias squared + variance is usually what you actually care about. Regularisation deliberately introduces bias for exactly this reason.
The standard example. Sample variance divides by n-1 to be unbiased. But the sample standard deviation - its square root - is still biased, because the square root is a nonlinear function and expectation does not pass through it. That catches almost everyone.