It wasn't.

In 1989 two mass demonstrations in Georgia were met with brutal attacks by Soviet troops, resulting in 38 civilian deaths and hundreds more civilians with non-fatal wounds (mostly gun shots).

In 1990 Azerbaijanis took over several border areas with Iran and began crossing the border, thousands of Soviet troops flowed into the region to restore control from Moscow, over a hundred civilians were killed and hundreds more were injured (the troops broke up demonstrations by firing into crowds). There was a tense standoff in the region between Soviet troops occupying Baku and the Azerbaijanis who were generally highly opposed to continued rule from Moscow.

In 1991 Soviet troops tried to keep Lithuania from breaking away. Soviet tanks were on the streets, facing off against Lithuanian civilians. In January Soviet troops seized several government buildings in Vilnius including the TV tower, during which 14 Lithuanian civilians were killed and over a hundred more were injured (many from being shot).

Similar events played out in Latvia at the same time, with six deaths and numerous civilian casualties.

In August of 1991 a coup by hard-line communists attempted to oust Gorbachev from power. Russian President Boris Yeltsin opposed the coup openly and drew the support of many military forces. Only a few deaths occurred in the tense standoffs over the few days before the coup collapsed.

In 1993 the constitutional crisis in Russia resulted in President Yeltsin facing off against the Russian Congress, culminating in a call from Congressional leaders to have the air force bomb the Kremlin (which were not followed through) and shelling of the Congressional building by armed forces loyal to Yeltsin. Several hundred people died (perhaps as many as 2,000).

In 1994 Chechnya tried to break away from Russia, which was met with a harsh military response, kickstarting an ongoing series of wars in the region that would ultimately claim tens of thousands of lives and devastate the region.

I've written about this before, so I'll just copy that here:

It wasn't necessarily non-violent. Civil war started in Tajikistan almost immediately, the Nagorno-Karabakh War between Armenia and Azerbaijan had been going on since 1988, Moldova had a brief war with Transnistria, and Georgia saw fighting between its separatist regions. Thousands died in these combined conflicts, and both Armenia and Azerbaijan are still shooting at each other today, while Georgia most recently fought Russia in 2008 over its regions, and the current Ukraine conflict could be argued as a legacy of this. But that's all too recent for here.

Now, I imagine you mean why didn't Russia engage in civil war or any major conflict. Well even there they had the 1993 shelling of the White House; that total conflict saw at least a couple hundred killed, possibly thousands. But in terms of 1991, I'd say that because the USSR was a federation, the 15 constituent republics (or 12 by that point, as the Baltics had effectively split off by then) were more concerned with their own future, and their problems are noted above.

Russia itself though was in a position to avoid conflict. Gorbachev worked until nearly the dissolution of the USSR to preserve it, using diplomacy and negotiation, as he was not widely supported in the military. This is evident by the coup attempt in August 1991, where hardliners within the government tried to overthrow him and preserve the USSR. That was probably the closest Russia got to an actual civil war, and indeed there were plans to fire on the crowds that had gathered to stop the tanks. Had that gone through, it would have been a massacre and more than likely resulted in a war. But fortunately common sense prevailed, and the coup was ended without any deaths.

Note also that I don't include Chechnya here, because the first Russian invasion only happened in 1994; prior to that Chechnya had been largely de facto independent, but left to its own by Russia. Though Russian forces were sent to Grozny in November 1991, they quickly retreated in the face of Chechen forces, and no shots were fired at that point.

Edit:

For anyone interested in a clear, simple look at the dissolution of the USSR, I'd suggest Moscow, December 25, 1991: The Last Day of the Soviet Union by Connor O'Clery. It gives a look at the events leading up to Gorbachevs resignation, interspaced with a full look at the date in question. Its a short book (around 300 pages) and a quick and easy read that will give anyone unfamiliar with the era a decent understanding of what happened.

There are more specific works detailing the post-Soviet conflicts, which can be provided if interested.