I understand that in MAE, because many small errors will drown out rare, but very large errors. Due to Squaring, MSE will quickly point out large errors.
My question is then why do we need MAE? Are there problems where MAE is better to be watched for?
Any examples for type of real-life problem where MAE better than MSE (and the other way also). The more intuitive the example the better. I am almost ok on the classification error types just because of the medical diagnostics test example fits it so well.
I am not a math guy and this whole topic makes my head hurt.