My Truth
Your Truth
His Truth
Her Truth
These are all misrepresentations of a very important basic bedrock concept embodied in a single word, "Truth".
What is Truth?
Truth is the unchanging, objective reality of what exists and occurs—the actual structure, properties, relationships, and behavior of reality as it is. It exists independently of perception, belief, opinion, feeling, consensus, language, or discovery. Human beings may perceive, understand, or describe reality incompletely or incorrectly, but our limitations do not alter reality itself. A statement is true insofar as it accurately corresponds to that objective reality, regardless of whether anyone recognizes, believes, or understands it.
When people start using ideas like "My Truth" or "Your Truth" they are getting into the realm of opinion an justification of actions and beliefs. There is no such thing as "My Truth", there is only THE TRUTH. This is important for many reasons, but fundamentally it is important because by distorting this definition a person may make an untruth sound true. It can convince a person to believe a lie.
Changing definitions of words is a tactic that has been used to great effect by political and religious activists from time immemorial. For a society to flourish and develop into maturity it must be able to articulate its discoveries, hypothesis, and philosophies. For philisophical and intellectual clarity it is necessary to have well defined meanings to words. A society cannot reason effectively about reality if its language systematically erases the distinction between what is true and what people merely believe, perceive, experience, or assert to be true. Undersatanding of these things by the general population is what, in theory, is supposed to govern it's decisions. The government should reflect the will of the people governed. If they are misinformed and or misled, they are much easier to steer into a path of the deceivers choosing. This is a big path to tyranny.
Truth is therefore valuable in and of itself. It should be treasured and verified. There is no harm in examination of truth because there is nothing for it to hide. Never pressure someone into failing to examine and question a statement or concept. If they desire clarity then help them verify the claim. You may come to a deeper understanding of the subject or, perhaps, even realize that you were wrong.