Regarding the South's secession, the US Constitutution does not say by what method, if any, such secession is to be allowed, so there's no clearly defined principle the Confederacy followed.
However, the tenth amendment says all rights not given to the Federal government are given to the states or to the People. "People" is pretty vague, but I'd tend to think if we're dealing with the secession of a state, "People" can only refer to the people in that state.
The People didn't vote directly on secession, no, but they did do so through their state legislaures. Maybe its a little wrong (Although considering he got only 40% of the vote, I don't really have a problem with it) to secede because you don't like the President, but its unjustified to wage a massive war over that, and besides, people have an intrinsic right to choose their own government.