and we didn't have a war. The ABM Treaty originally allowed each country to build two ABM sites. They later amended it to one site each. We built ours to protect one of our missile fields, preserving our ability to retailiate in case of an attack. The Soviets built theirs around Moscow, with the implication that there is no need to protect missile silos if the missiles are launched first. We deactivated our ABM system a day after it became operational*, but the Soviets (later Russians) kept theirs active all this time.

Having a defense doesn't necessarily imply that people would be more likely to use offensive weapons. At the height of the Cold War, the US had over 1,000 ICBMs (1052, if memory serves) and the Soviet Union had upwards of 1600. Many of these missiles had multiple warheads. At no time did either side have more than a handfull of ABMs, so the mere presence of an ABM system wouldn't make either side more likely to launch an attack. Both sides knew that they would suffer a massive counterattack regardless of the existance of an ABM system. The US, with its ABM system, sought to ensure that Mutual Assured Destruction (MAD - an appropriate acronym if there ever was one) would continue even if attacked. The Soviet strategy was to ensure the survival of their chain of command in Moscow.

*The Safeguard system consisted of two types of interceptor missiles, the Sprint and the Spartan. The Sprint was an extremely high acceleration (several hundred gees) point defense system designed to go after warheads just a few seconds from impact. The Spartan was a longer ranged interceptor designed to go after warheads while they were still 200-400 miles away. Both missiles were tipped with nuclear warheads (as are the Russian interceptors) because they weren't accurate enough for a kinetic kill. Those warheads were a major problem, though, because of the Electro-Magnetic Pulse (EMP) effects. Firing our own missiles would've caused huge EMP problems across much of the country. That's why all of the ABM development since then has been in area of kinetic kill vehicles accurate enough to hit their target directly.