It depends largely on how one defines "winning," though most southerners don't think they "won." In fact, I might even go so far as to say that those who think so are just poorly educated, and honestly just don't know the answer. It is also possible that when they say "they" won, the still mean that the North won, though how exactly that could be eludes me.

An argument can, however, be made that the Union did not really "win" the war. If one views the war as a war to keep the United States from splitting in two, as it was portrayed at the time, than indeed the North won. The same is true is the purpose of the was is seen to be the elimination of de jure slavery. If however, one considers the objectve of the North to create real and lasting change in the lifestyle of former slaves, the issue becomes a bit murkier. Black Americans were almost universally disenfranchised in the South, and indeed much of the country following the Civil War's end. It wasn't until the Civil rights movement almost 100 years later that that significantly changed.

Why anyone would want to consider the American Civil War a Southern victory evades me, but it can certainly be viewed in a certain light as an incomplete victory by the North.

They're not southerners but one person who holds this view is historian/military author Tom Ricks, who has primarily written about the War on Terror.

He borrows a phrase from that conflict, the idea of "Phase IV Operations," namely the stability/occupational phase and says that in the Civil War major combat operations (Phase III) ended in 1865 but we lost phase IV, or at least didn't win until 1964.

In other words the failure of reconstruction, the emergence of the Klan, and segregation meant that we won the war but lost the peace.

I seriously doubt that's what your southerners are talking about, however, but it is a view that's worth considering from a major military thinker.

http://ricks.foreignpolicy.com/posts/2010/09/21/when_phase_iv_of_our_civil_war_ended http://ricks.foreignpolicy.com/posts/2014/04/25/sherman_xi_the_confederates_i_worry_about_most_after_the_war_will_be_the_young_men_