I will offer a (hopefully moderate) defense of the Union's prospects.
Are the Confederacy's chances zero? No. Yes, the Union has an advantage in men and munitions but that merely makes it implausible for the Confederacy to win, not impossible. Lincoln and Hamlin could get typhoid, a meteor could hit D.C. and the Confederates could even rustle up better battle commanders in the West that Braxton Bragg and Leonidas Polk.
On the other hand, Confederate victories as usually spelled out fall into three main categories, all of which ring somewhat false to me.
1- Lee wins at Antietam, or Gettysburg, or somewhere else, and then goes North and the jig is up. Quite simply - it's really hard for Lee to make the Army of the Potomac simply evaporate at any point in his career. Beat it (with proportionately almost as bad casualties?) sure. Completely smash it to bits, when he has less men and the opposing general isn't John Bell Hood? That seems of doubtful probability. (I think there are a few times where a Cannae could be achieved but the timing needs to be better than just picking Antietam or Gettysburg).
And at this point in time, Lee just waltzes into Washington? Even if he takes it, what then? Lee's Army camps there and the North is like "gee, can't possibly think of what we could do to Lee's army sitting here, guess he achieved a win condition?" This outcome seems to be based on a series of improbable events.
2- Trent Affair intervention. This isn't a knock on the people writing Trent Affair timelines right now, far from it (Please keep writing, actually

). Three of the four I've seen are well researched and, with some variance in speculation, put a lot of effort in thinking how things are going to pan out when the U.S. and Britain get involved in total war. (The fourth one gives Kansas to the Confederates but I digress.)
My opinion is that if it comes to total war, yes, Britain and the C.S.A are together going to beat the United States on sea and on land. I simply think that scenario is vanishingly unlikely. Yes, there was a crisis in OTL, but it was averted for a reason.
Britain and the U.S. each have nothing to gain from going to war. Lincoln is not an idiot; he's not going to insult Britain and he's going to make any concession short of war if he has too (sure Seward had strange ideas but the rest of U.S. policymakers are not as blindly hawkish as he is. Hawkish, yes, but not enough so to take on two enemies at once). And from Britain's perspective, what real reason do they have to go to war over the South? Innate sympathy with slaveowners was not the sentiment of the time, and if Britain really wanted to go to war over balance of power than they would be best suited to look at Bismarck in Europe and not the U.S. an ocean away. Britain's advantage over the U.S. is (I don't want to stretch analogies too far) like that of France over Mexico in the same time period. If they really put in the effort of course they are going to beat the United States; but there is no logic to them doing this, so barring Palmerston being very stubborn on points of pride they have no reason to stay in the war.
3- Peace of exhaustion. Aka, Hood or Johnston prevents Sherman from taking Atlanta and George Pendleton (or some other go-to peace Democrat) wins in 1864. (Britain could swoop in to force a peace treaty here, but again, why would they care enough to put boots on the ground?) Firstly, the south is going to get carved up like a ham if they are lucky enough to actually get a treaty recognizing their independence from the Peace Democrats. Secondly, a slow high-casualty advance is still an advance. This outcome requires the northern leadership either being willfully blind to the fact that they are still winning the war, or just deciding "yes, we could win back half of our country in a few years. But we'd rather not suffer the casualties from that." The Confederacy in 1864 and 1865 is still going to be losing men at a greater rate - the Union being bled dry is just not a realistic outcome and the 1800s U.S. isn't exactly known for it's concern for humanitarianism in war. So unless the Confederates actually reverse the tide of war (not merely create more Overland Campaign-like bloodshed), they can't win.
So of course the South has a shot at winning the Civil War (and if Britain really cares enough then the South will win), but I think we need to remember that the Union is not going to make willfully stupid decisions to reach that end. A southern victory will require the South not collapsing in the west, probably a Union army being captured wholesale in the east, and Britain and France gently reminding the U.S. how fucked it's economy will be. A combination of factors, in other words.
Sorry for the word-dump. At the end of the day it's all just discussion and I don't think anyone has malicious motives behind their arguments.