I can't give you all the answers, but I'd like to discuss people's objections to it, as well as why I still believe it's a worthwhile philosophy. Not looking to change minds so much as to have an exchange of an ideas. Or at least provide an understanding of how I and most Marxists I know think about politics, the damage done to the idea of Communism by the USSR and governments like it, economics, etc.
Why has every communist state to date been authoritarian? Can communism and democracy co-exist?
The goal of communism is economic equality for all, which is an important basis for actual, direct democracy, in my opinion. Everyone's opinions on a situation, no matter how different they may be, all have equal weight. One person, one vote. Not one person one vote, one corporate executive, one entire election skewed in favor of said executive's interest.
As for why every communist state has been authoritarian, most Trotskyists will blame Stalin and his attempt to bring about the socialism in one state policy. A truly communist government cannot coexist alongside a capitalist one due to the latter's aggressive need for imperialist expansion...and the reason for Stalin's brand of authoritarianism and aggressive expansion of his ideology to other countries was because he needed an economy to prop up the USSR alongside its free world mirror, at the expense of millions of wasted lives.
However, communism and democracy did famously coexist in two places, if I recall correctly: the initial aftermath of the October Revolution, when proletarian soviets wrested control of the Russia from the bourgeoisie provisional government created after the February Revolution in order to nip communism in the bud, and the Paris Commune, which existed for a two months until the Third French Republic fell to the Prussians in May of 1871: this particular example is often referred to as a dictatorship of the proletariat, which could have led to democratic communism if France wasn't at war.