What you said
Perhaps your principal is saying that he or she favours a more distant, authoritative relationship, rather than a slightly more intimate one where teachers show more of an interest in the personalities of their pupils. I think that building a positive relationship with classes is crucial.
It sounds like your head is more concerned with exam results than young people as individuals. While the relationships between pupils and teachers shouldn't be focused on to the detriment of other important pedagogy, they are important to foster learning. A relationship does not have to be friendship, but can be the dialogue between two parties, which is the glue of the learning and teaching process.
The expert view
Every time you meet someone there is a relationship, so it is pointless to suggest relationships are not created between pupils and teachers. The question is not "Do they like me?" but "Are they learning, and safe?" The irony is that many pupils eventually start to like teachers with whom they learn and behave, because they respect someone who lays down the law and helps them.
The other misunderstanding in terms of relationships is when teachers are told to "build relationships" with a class that is being horrible. This is closely linked to the mistake of believing that, if the pupils like you or are entertained by you, they will be great pupils and learn loads. This is not so. I think the trigger statement indicates that too much is being made of some aspect of the relationship.
We are not here to please pupils, although if that happens incidentally that is OK. The relationship we need to have with them is that of adult first and educator second. If that has been established, you are perfectly placed to teach them. And that is the core of our job.
Tom Bennett's latest book, Teacher, is out now, published by Continuum.