I think it's because he grew up in that institution that he knows how toxic a lie can be, and how the firm never stood up against lies, and as they say, a lie can travel half way around the world before the truth even gets a chance to get it's shoes on. We know this from the 'Meghan made Kate cry' lie.
I think it is precisely because of his growing up in it that he is determined to be the one to break the cycle.
I would give that interpretation more credence if he & MM got basic facts correct, or even agreed between themselves about basic factual accounts of things, but they don’t. For example, even in a televised interview they differed over how many family conversations concerned their baby/ies’ skin colour, and when the conversation/s happened.
I think what it is is that Harry, like his mum, is more emotional than fact-orientated. If something “feels true” to him, he goes with that. Similarly, MM caused confusion by saying they married three days before their official ceremony. It seems it was unofficial vows, not a wedding, but she decided to regard it as a wedding so she called it a wedding. Cue much confusion.
The palace, OTOH, is full of people paid to be very precise and accurate and avoid untruths or misunderstandings.
Those two styles are bound to collide.