As with anything, it's hard to generalise without oversimplifying, but here goes. You don't generally just have a data set and a machine learning algorithm that somehow magics outputs from a data set. Usually decisions have to be made by people either in training the model, selecting variables that are included in a model, etc.
Here's a simple example. Say you're trying to come up with an algorithm that decides whether articles in a data set are "fake news" (topical, I know). We have to tell the algorithm whether a given article in the training set is fake or legitimate, otherwise how would it know? Clearly this will reflect the views of whoever is tagging the articles. When we run the model on a training set we need to score how well it did, again this will reflect the opinion of the person doing the scoring.
Here's a simple example. Say you're trying to come up with an algorithm that decides whether articles in a data set are "fake news" (topical, I know). We have to tell the algorithm whether a given article in the training set is fake or legitimate, otherwise how would it know? Clearly this will reflect the views of whoever is tagging the articles. When we run the model on a training set we need to score how well it did, again this will reflect the opinion of the person doing the scoring.
For a real example: https://mathbabe.org/2016/05/12/algorithms-are-as-biased-as-....