The word "democracy" should be defined before this question is answered. Merriam-Webster's dictionary reads that "democracy" is "a government in which the supreme power is vested in the people and exercised by them directly or indirectly through a system of representation usually involving periodically held free elections."
Many people believe that, as a political system, the United States is a democracy. It is not; it is technically a constitutional republic, but it does fit the Merriam-Webster definition of democracy above. In the United States, citizens vote to elect their fellow citizens to be their government officials and represent them in the legislative, administrative, and executive affairs of the state. This does not mean that the majority always rules, and it certainly doesn't mean "mob rule." Hence, it is called a "representative democracy."
The Soviet Union had a different kind of system. In the Soviet system, committees were formed to administer legislative and executive decisions on behalf of the citizenry. This is not "representation" in the same sense as America's "representative" democracy, because the committees making the decisions were not elected by the people nor sent by the people to represent the "will of the people." It should be noted that the Russian word "soviet" is translated to English as "council" (akin to "committee" or "assembly"). Hence, the Soviet Union was a government by committee. A big difference between the United States and the Soviet Union is that the USSR did not hold "free elections" as used in the Merriam-Webster definition above. Hence, they "did not like" democracy, using the words in the question above.
The nascent Soviets (the Bolsheviks) formed through grassroots assemblies and underground meetings in which they became revolutionaries against the bourgeois status quo, the decadent monarchy, and the owners of the factories who controlled the means of production and hence capitalized on and exploited the labor of the common workers. The meetings were originally formed by dissatisfied urban industrial laborers and were influenced by Marxist communist ideology in which "the people," the exploited workers, would take over and rule the government. Their goal was a "dictatorship of the proletariat," from which a worker's utopia would form for workers all across the world. So, it can be argued that the Soviets clearly cared about the well-being of the common man and his place in government rule.
Therefore, the communist Soviets were not against "the people" or "democracy." Demos is roughly translated from the Greek to mean, "the common people of a country," and -cracy means "the rule of"; after all, the words communism, community, committee, and common all share the same roots and elicit images of a healthy society and social harmony. The Soviets even called themselves “the society of true democracy." In conclusion, it is inaccurate to say the Soviet Union "did not like democracy." In fact, the political system of the USSR was called a "council democracy".
It might be worth asking a related question to the one you've posed: Was the Soviet Union actually as ideologically opposed to democracy on its own terms as we tend to assume? It's an interesting question, and one worth thinking about in and of itself. If you've ever read the novel Darkness at Noon, this is actually a theme that comes up in its treatment of Rubashov, who was himself a stand-in for the first generation of Bolshevik leaders (later betrayed by Stalin, sacrificed to the Revolution). What we see depicted in that book—and I think it's frighteningly accurate to history—is an undercurrent of pragmatic calculation by which the Party demands sacrifice in the name of the Revolution, all for the supposed purpose of creating a future utopia (and this is a key theme central to understanding Marxism: it's ultimately utopian in its aspirations). This raises the question: if the single-party dictatorship is understood ideologically in terms of being a means to utopian ends, could that future utopia itself be democratic?
In any case, I would suggest that one of the critical issues here is the degree to which Western democracy has historically been tied up with capitalist economies as well as imperialist exploitation. This means that communists would certainly have found much to be suspicious about, as far as Western democracies were concerned. Furthermore, consider the history of the Bolshevik Revolution itself and the degree to which Western democratic powers interfered by supporting the White Army. Of course, Western powers had reasons to distrust the Soviet Union as well given its internationalist vision of communism and the vocal internationalism represented by someone like Trotsky, who argued in favor of global revolution. Both sides would have pictured this in terms of an ideological clash between the liberal powers of Western Europe and the United States on one side and the communists on the other.
As one last subject worth thinking about, I'd suggest you factor in the ideological split within Russian communists. While the Mensheviks believed that the movement should be populist in nature, the Bolsheviks believed it should be driven by a professional elite dedicated to the revolutionary cause. Naturally, it was the Bolshevik position that ended up shaping communist Russia, and once the Bolsheviks took power, this elitist vision of the revolution resulted in a very hierarchical political structure by which power and authority emanated from the Communist Party.