Trotsky was an internationalist. His idea was that the world ought to be made safe for communism. To that end, he was in favor of raising a huge army of communist workers and running roughshod over Europe.
He failed to understand that the reason - virtually the only reason - that the Bolsheviks had won over Russia was that the peasant troops that made up these armies were sick to death of war. He tried to move on Poland, as a first step in this war of "liberation". The Spartacists followed with riots in Germany. The whole enterprise failed miserably; the workers of Poland rose up against this "people's army" of the new Soviet Union, and although outnumbered, crushed it. Twenty years would pass before the Bolsheviks would enter Poland again; five more, before the place was roughly assimilated into the Communist bloc. In Germany, the revolutionaries so offended public sensibilities that citizen militias, called freikorps, formed up of their own accord. With little help from the government, which was practically paralyzed after the loss of WW I, they alone were able to supress it. The backlash of all this ended in 1933 with the rise of Nazi Germany (the German communists actually supporting their election, in the hopes that it would trigger another civil war).
In any case, after 1922 Trotsky's plans of world conquest had obviously fizzled; the clout he had gained from being the mastermind behind the defeat of the Whites was badly tarnished. Being a horrendous administrator otherwise, he eventually had to flee Stalinist Russia. He spent the rest of his days lambasting Stalin, until finally assassinated in 1940.
Tutachevsky was a better general, and Trotsky wasn't much more than a political general anyhow. As a theorist, he had much in common with most dictators of the day - basically, that war and conquest can be made to solve everything.
If you want to discuss a leftist that was truly a decent man, why not discuss Kropotkin? If you really believe in a decentralized state, why not mention Machkno? Or is holding to the party line so important that you can't even make an honest fight of it?
P.S. Teddy Roosevelt was, of course, better than the lot of 'em. Bully.