It comes down to a weird strategic balance somewhat similar to the idea behind anti-ballistic missile treaties. Effectively, the strategy of nuclear deterrent relied on having the ability to retaliate with enough force should one side realize they're under nuclear attack. With longer ranged missiles, traditional means of detecting nuclear attacks would provide a fairly long lead time (something on the order of half an hour) that would give friendly nuclear forces adequate time to launch their weapons. With shorter-ranged missiles, both sides had sufficient strategic depth that deployment of such weapons would require something that would provide an obvious warning of attack (like masses of bombers scrambling towards potential targets). This same reasoning requires a brutal calculus with respect to warheads. On the simplest terms, strategic nuclear exchanges rely on one side's ability to defeat the other's ability to retaliate in kind by hitting command and control centers, early warning networks, and delivery platforms themselves.

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Intermediate-range nuclear weapons cause this to break down by providing the range to hit important targets from friendly territory while having a short enough flight time so as to make timely response very difficult. In the context of the Cold War, missiles like the Pershing II and SS-20 had flight times of as little as 10 minutes. For Moscow, this was a major issue, as the Pershing II (as well as the GLCM) would put many strategic targets in the USSR in range, meaning the US had the potential to hit many strategic targets - potentially even Moscow - before leadership could reasonably respond. For the Soviets, the SS-20 put much of Western Europe within range of platforms that weren't covered by the SALT agreements, meaning there was the potential for the Soviets to strike strategic targets in Europe with missiles not covered by SALT, thus freeing up missiles that were covered by SALT for more important targets elsewhere.

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In the context of the Cold War, the deployment of the SS-20 and Tu-22M by the Soviets marked a major escalation of the Soviet nuclear threat, and NATO would respond by deploying Pershing II missiles and GLCMs to maintain parity. Both sides would recognize this as untenable and work on talks for a treaty to limit such platforms by the early '80s, ultimately coming to an agreement by the end of the decade. Since then, however, the strategic landscape has changed. The INF treaty was between the US and USSR, and although Russia was covered by the treaty after the USSR collapsed, China was not. Unfortunately that's as far as I can go without breaking the 20-year rule.