Why is Mean squared error a good loss function? I am currently studying the statistics behind machine learning and my question is why the mean squared error is a good selection for the loss function? Does it have good statistical properties (unbiased, consistent)? Or practical advantages?
Someone told me that it is unbiased but I still do not see why it is even a estimator, since it is rather a function which evaluates your point estimator. I would appreciate any type of clarification since I could not find anything online about this topic.

Based on your last comment about “likelihood”, “unbiased”, and “estimator”, I think I know what your interviewer meant.
When you assume $iid$ Gaussian error terms, which is a common assumption, in linear regression, minimizing square loss gives the same solution as maximum likelihood estimation of the regression parameters. That is:
$$
\hat\beta_{MLE}=\hat\beta_{OLS}=(X^TX)^{-1}X^Ty
$$
Further, even under milder conditions (don’t even need Gaussian error terms), the Gauss-Markov theorem says the OLS solution is the best linear unbiased estimator (BLUE), where “best” means lowest variance (among linear and unbiased estimators).
If you drop either the linear requirement or the unbiased requirement, you can get lower variances, however. For those (and probably other) reasons, square loss might not be the best estimation method. As another comment remarked, there is no silver bullet.
