The thing is that steel was difficult and expensive to make in large quantities until a number of processes like the Bessemer Process were invented starting in the 1850s, and barbed wire really needs to be made from steel to be effective.

Wire made from iron and other materials has been around for thousands of years, but none of them are really suitable. The only material that is close to suitable is wrought iron. Any other metal will be too brittle (cast iron), too soft (copper) or too expensive (anything but iron, until cheap aluminum comes around, but that is too weak).

Wrought iron isn't as good of a choice as it seems though. It is more difficult and expensive to produce than mass produced (such as Bessemer) steel, has less tensile strength, and rusts faster due to a higher level of surface deformities (again from the working it must go through.)

So in essence, barbed wire as we know it today needs to be made from steel, which wasn't cheaply and widely available until the mid-19th century.

http://www.efunda.com/materials/common_matl/common_matl.cfm?MatlPhase=Solid&MatlProp=Mechanical

http://www.madehow.com/Volume-2/Barbed-Wire.html (link included for the patents, all in the 1860s)

The problem with asking this kind of question is that you have the benefit of hindsight. You know how cool it is, yet, they didn't. Example: Why was youtube invented so late in the internet revolution, why not in the 1990s? Same kind of question.

One likely answer is that people were used to fencing like they had used for generations. It was one of those things that when Joseph Gliddon made the first barbs in his coffee maker that a lightbulb just came on.

Also, until he demonstrated it, many people believed that barbed wire wouldn't stop cattle.