It is hard to remain cool headed and rational about it. But at least try, or get a third person to give you some candid feedback.

If the PIP is merely a form of being soft-fired, then give it a token effort and seriously look for a new job.

If there really is room for improvement on your part in some specific area, then why not work to the program and see if you can make an improvement? I would still start looking for new work as a plan B.