This happens in almost every trial.
You spent a great deal of time, energy and money to create exhibits that will help the jury understand key issues in the case. You might create enlargements, also known as blowups so that the jury can see the medical records sitting five or six feet away. You might use anatomical models. You might use diagrams and records on your laptop and project them on a screen.
There are many ways to use exhibits matched only by your creativity. Your exhibit may be so good that when the defense attorney gets up to cross examine your witness, he turns to you right before he starts questioning and says “Mr. Attorney, you don't mind if I use your exhibit to question your witness, do you?”
If I say “I do mind, and you have to use your own,” I now look selfish in front of the jury. The jury may question and wonder why I'm not allowing my adversary to use my own exhibit. This is especially true when I have used the exhibit to question my witness.
It would be very awkward for me to turn around and say “No you can't.”
Likewise, if the defense creates an exhibit that works well and I think would benefit me, I will also do the same to the defense attorney.
“Mr. Defense lawyer, can you turn on your laptop and the projector so we can all see the record you were referring to as I question your witness?” Grudgingly, the attorney will likely agree.
If the attorneys become petty and do not allow each other to use their exhibits at trial, the jury will be left to wonder why there is this back-and-forth bickering and why aren't they simply sharing the exhibits for the purposes of getting the witnesses to answer the questions.