For the next decade, roughly 1984 to 1994, both the Internet and the PC grew by leaps and bounds, the Internet as a highly connected but very exclusive technology, and the PC as a highly dispersed but very inclusive technology, with the two hardly intersecting at all. One revolution for the engineers, another for the masses. The thing that changed all of this was the Web. Which is how we got the mess we have today. In 1994, the browser created sudden pressure to wire the world's PCs, in order to take advantage of the browser's ability to make the network easy to use.
Servers are the net's first-class citizens, with real connectivity and a real address.
As both Gomes and Katz noted, P2P means many things to many people. PC users don't have to be second-class citizens. Personal computers can be woven directly into the Internet. Content can be provided from the edges of the network just as surely as from the center. Millions of small computers, with overlapping bits of content, can be more reliable than one giant server.