I have taken a number of employees through capability processes previously, and overseen the process in many more cases. I don't think I can recall one person who ever agreed that their performance was a problem, even when it was glaringly obvious to everyone else and there was shedloads of evidence to prove it.
Your manager may have another agenda here, but why would they? It's a major hassle to take someone through this process, and I honestly can't think of any reason why a manager would choose to subject themselves to that if they didn't feel that they had to. If someone is actually doing their job well, that is a reason to celebrate because the manager can get on with other things.
The PIP should state specific areas where you need to improve and clear, achievable, measurable success criteria. If you know that you're capable, make sure that you're clear about what's expected and ensure that you deliver it.
If you spend your time arguing the toss about how your performance is fine and your manager is wrong, they will just move towards managing you out. Unfortunately for you, the workplace isn't s democracy and it is your manager that gets to set the standards and expectations for your role, whether you agree with them or not. That said, the expectations do need to be reasonable for your role, the targets need to be transparent and achievable, and you should be offered any support that you might need in order to meet them.