Our current Internet runs on the TCP/IP protocol suite that was designed for use in the ARPANET, which completed its switch from the old Network Control Program (NCP) to TCP/IP on January 1, 1983. There's an interesting paper by David Clark called "The Design Philosophy of the DARPA Internet Protocols" that describes how TCP/IP came to be. We can also trace some of the security problems that have plagued the Internet since its beginning to the design criteria that this paper describes. The ARPANET was retired in 1990, but we're still feeling its influence today.
This paper tells us that there was a single fundamental goal in the design of TCP/IP and seven second-level goals. The fundamental goal was this:
The top level goal for the DARPA Internet Architecture was to develop an effective technique for multiplexed utilizations of existing interconnected networks.
There's probably no way that you can interpret that as laying the foundation for today's security problems. The second-level goals are where this creeps in. Those were the following:
1. Internet communications must continue despite the loss of networks or gateways.
2. The Internet must support multiple types of communications services.
3. The Internet architecture must accommodate a variety of networks.
4. The Internet architecture must permit distributed management of its resources.
5. The Internet architecture must be cost effective.
6. The Internet architecture must permit host attachment with a low level of effort.
7. The resources used in the Internet architecture must be accountable.
The last three of these are the ones aren't quite what today's business use of the Internet needs. In particular, cost effectiveness can be detrimental to security, a low-cost of attachment can be detrimental to quality-of-service guarantees, and accountability can be detrimental to efficiency.
You might argue that being cost effective doesn't really conflict with being secure if the costs of not being secure are properly accounted for, but security just didn't seem to be a concern of the architects of TCP/IP.