First of all, P2P is the process of performing cryptocurrency transactions directly between two people without middlemen and third party intervention. It allows you to determine your best price.
Always this myth that if you go to a platform that calls itself a p2p exchange you're getting rid of intermediaries and these 3rd parties.
It's not like that unless you use a completely decentralized platform, with no central server and you do your transactions face facing in cash, if no then you're still at one point relying on a third party.
Take for example this deal on Binance, if you went to binance p2p and you selected to buy coins and pay the guy via WU or Paxful or bank transfer then you have used:
- a middleman, the platform where you have met your buyer
- a third party, the bank, Paxful, WU, or whatever other payment services you used
True p2p means you gave the guy coins he gives you the money, there is nobody that can freeze that money, (like a bank or Paxful) and there is nobody that facilitates that meeting so if that middleman is gone (in this case Binance's website) you can still deal with your buyer as nothing happened.