How come you never show them the evidence? Is it because it lets the lawyers concoct a story?
Apart from anything else, it creates information asymmetry - your opponent certainly won't tip their hand to you until they feel the time is right.
And you leave yourself open to bluffing. If you blab everything, and then the other side steps it up and comes after you harder, you'll be left wondering - they know everything, but they're doubling down - am I missing something? Gee, they must have a stronger case than I thought.
I’ve had people tell me outright lies, which puts them in a difficult negotiating position when you can prove it. But the lies would not have been told (and my negotiating position not strengthened) if all the evidence was laid out up front.
Hiding information from an adversary has few downsides, as long as you keep your goals clear. You can always provide more information later. But you can never take information back.
In hindsight, it may not have mattered. After all, I was going up against lawyers. thathndude, who has the top comment and is a lawyer, has a different perspective.