The most classic example of subjectivity is revealed in dreams. Each persons’ dreams are completely unique. As an experiment, try to write down what you saw and experienced in your dream today morning. It is incredibly difficult to express it in words. You would have to use all kinds of analogies which are again based on your previous experiences. You may even need to diagram out some stuff, but it would still just represent its skeleton.
I think art forms exist only because of subjectivity. Is everything was objective there would be no art. Each of us sees different patterns in this matrix of reality. Artists are able to extract, articulate and communicate these patterns to us, rich in emotional value. Art is a form of communication. It can communicate subjective experiences in ways that verbal, math or logic cannot.