Bob hit John in the face.
Based on that information alone it seems like an unprovoked attack in which Bob is an aggressive attacker. Yet the statement is still factual.
Bob hit John in the face because he was choking Mary to death.
In this statement we see Bob as the defender and not the aggressor. With more information we could see why the situation unfolded in the first place, but many times it won't be available and things get left to interpretation.
To agree with what you are saying above, large parts of human life are subjective, not because reality is subjective, but because information loss leaves us to interpret events via our biases.
One of the strangest criticisms I see about WP is that it's subjective about things like politics or biographies. These are subjective topics, and as such it's impossible to be wholly objective about them, even from the most well-intentioned, educated, neutral point of view. It's a strange criticism, because usually the critic will have no problems in ignoring the subjectivity of their suggested alternative, or sometimes conveniently neglect to provide an alternative at all.
Fundamentally compiling an encyclopedia is an act of summarising - declaring certain information to be more important, interesting or relevant - and it is impossible to eradicate subjectivity from that.