My understanding is that both Gorbachev and Reagan talked about complete nuclear disarmament with both of them saying they wanted to eliminate all nuclear weapons by 2000. However, Reagan wanted to retain the right to eventually deploy SDI while Gorbachev wanted to limit SDI to a research project at the most.
If both the United States and Soviet Union would destroy their nuclear weapons then how could SDI be a threat?
Did Gorbachev fear that any weapons ban would be ineffective like 1970s Biological Weapons Convention? Did he fear that SDI was more then just an antiballistic missile system? Was it just a case of political target fixation?
The book you want is The Dead Hand: The Untold Story of the Cold War Arms Race and its Dangerous Legacy by David Hoffman. He won the 2010 Pulitzer Prize for nonfiction with that book, and it contains a section that addresses your question. To paraphrase Lawrence Freedman's 2010 review of the book in Foreign Affairs, you should walk carefully when considering any book that claims to be the "untold story," but Freedman actually backs it up.
He dissects and discusses a series of internal documents collected by Vitaly Katayev, a Soviet aviation and rocket designer who worked as a staffer for the Central Committee of the Communist Party of the Soviet Union. That's a killer source, and it it hadn't been really dissected before Hoffman wrote about it. The papers are now at the Hoover Institution Library and Stanford University archives.
The summary of the matter, according to Hoffman: "He didn't want an arms race in space."
When intelligence agents uncovered the scope of SDI, Gorbachev's advisers told him it was technically feasible, but the necessary science and engineering was at least two decades away. They didn't think SDI would work in the 80s, but why then was the U.S. planning to spend billions on it?
Within weeks of taking office, Gorbachev received a proposal to build a Soviet SDI system. It would have been a massive program that would have ensured the Soviet Union would spend a gigantic portion of its economy on military projects for decades to come. That was completely against what Gorbachev was trying to do domestically.
For similar reasons, Gorbachev shot down an idea to put up to 38 warheads atop each SS-18 missile ─ by treaty they were limited to 10 warheads ─ he was concerned about the economic effects.
Building on what /u/The_Alaskan has written (and based on the same source — Hoffman''s book is great) — in the US we tend to think of the USSR as being a totalitarian, monolithic state controlled by the Party Secretary (in this case, Gorbachev). In reality there were more players involved, especially in the later periods. Gorbachev was trying to wind down the military expenditures and get the country on a better path. The military of course was not so interested in this approach. If the US was pursuing space weapons (and while Reagan pitched SDI as purely defensive, the line between defense and offense is basically non-existent in this case as with many) then it would give the military and oppositional forces within the Soviet government major leverage to push for their own programs and their own work, putting Gorbachev in a very uncomfortable box.
Separately, if SDI actually did work, it would be massively destabilizing. It would give the country that controlled it a first-strike capability if they chose to develop it. Reagan promised Gorbachev that he would give the Soviets the technology once it was developed, but Gorbachev (wisely) thought this unlikely to be actually feasible. (He pointed out that the US did not even allow the Soviets to have agricultural technology they had developed.) And even if Reagan himself had wanted that sharing to occur, there is zero guarantee and almost zero likelihood that Congress, or a future President, would follow through on such a loose promise.