No it is not p2p. You cannot download a coin like an mp3 file. There is no file sharing.
Yes good, you noticed. Bitcoin is not a file sharing network, it is a payment system.
I can send a Bitcoin to you and you can send a Bitcoin to me.
We have equal rights in the Bitcoin payment system : we can both pay and receive a payment. This is p2p.
With VISA or MasterCard : you have to pay for a terminal, pay a yearly subscription and fees to receive a payment. The sender and the receiver do not have equal rights, this is not p2p.