It seems to be a tactical victory for the Union to the same extent that Gettysburg was a victory for the Union.

This is the source of your confusion. While many would agree with that statement, here's what the US Army has to say about it (from The Soldier's Guide: The Complete Guide to U.S. Army Traditions, Training, Duties, and Responsibilities:

In tactical terms, Antietam was a draw. General Lee's army was severely outnumbered at the outset and his enemy, Major General George McClellan, knew his invasion plan, yet the Confederates still held the field at the end of the day. But the terrible losses Lee sustained meant he could not continue operations on Union territory without risk of complete destruction. Lee's resulting withdrawal from Maryland was a strategic victory for the Union and provided Lincoln the opportunity to issue the Emancipation Proclamation.

So that's one argument that Antietam was a tactical draw, but a strategic victory. In Landscape Turned Red: The Battle of Antietam, Stephen W. Sears echoes this sentiment, and also provides a deeper look into that argument. He starts with McClellan's opinion of it (McClellan was obviously pretty biased, being the Union Commander and all...):

Our victory is complete. The enemy is driven back into Virginia. Maryland and Pennsylvania are now safe.

That was what McClellan told General Henry Halleck, General-in-Chief of all Union armies. If you thought that was a bit too optimistic, look at what he wrote to his wife:

I feel some little pride in having, with a beaten and demoralized army, defeated Lee so utterly and saved the North so completely. I am confident that the poison still rankles in the veins of my enemies in Washington, and that so long as they live it will remain there...I have the satisfaction of knowing that God has, in His mercy, made me the instrument for saving the nation.

(Jesus. Can you imagine what his Twitter feed would have looked like?!)

It's a good thing Halleck never saw that second letter, cause he was very unimpressed with McClellan's "complete" victory:

The long inactivity of so large an army in the face of a defeated foe, and during the most favorable season for rapid movements and a vigorous campaign, was a matter of great disappointment and regret.

President Lincoln agreed with Halleck and removed McClellan from command, replacing him with Ambrose Burnside. (Don't even get me fucking started on that guy...)

Sears finally takes the emotion out of the equation (thank god) and responds with:

What had been won and lost on Antietam's bloody field was not so quickly measured as McClellan imagined. Judging those twelve hours of desperate combat on a purely tactical level, for example, the Army of Northern Virginia could justly claim a victory. It had beaten back a foe much superior in manpower and ordnance and inflicted substantially greater casualties than it suffered. Except for the mix-ups that caused the Sunken Road to be abandoned prematurely, the severest military critic would be hard pressed to find fault with the way the Confederate high command conducted the battle.

That's a pretty good analysis of it; there were no huge blunders from Lee like there were at Gettysburg. The battle of Antietam ended with A.P. Hill's division showing up to stop the IX Corps in its tracks, while Gettysburg famously ended with Pickett's Charge, a massive blunder that crippled The Army of Northern Virginia and arguably turned the tide of the entire war.

A third source, the state of Virginia, also disagrees with you and McClellan:

I described the battle as a “draw” on the battlefield, if also a strategic victory for the Union. This is not an unprecedented claim...

But you and Little Mac might still be right! Because here comes Thomas G. Clemens to the rescue! He did a fantastic job of editing and annotating Ezra Carmen's** Maryland Campaign of September 1862, and he completely agrees with you:

If Gettysburg is a Union victory, where Meade merely held the field, then how can Antietam be a “draw” when McClellan AGGRESSIVELY attacked Lee all day long and, like at Gettysburg, Lee took a day to organize his army and withdrew the next day? I dare you to describe Gettysburg as a “draw”!!!!

That was his response to Encyclopedia Virginia's interpretation of the battle, and I'm guessing that probably aligns pretty closely with your view. The wording itself is very casual and emotional in the moment, but I assure you Clemens is a brilliant analyst and he is very good at what he does. Please read Carman's book and take note of what Clemens brings to the table. It's fantastic.

So I hope I've shed some light on the problem. Your claim that Antietam was a tactical victory on the level of Gettysburg makes a lot of sense to a lot of very smart people. But others have a problem with that statement, and with very good reason. Both sides raise many good points, and Antietam (like much of McClellan's career) is still very much up for debate. With all of this disagreement and debate surrounding the subject, "it was a draw" is simply the path of least resistance. It wasn't Cold Harbor, it wasn't Fredericksburg, it wasn't Shiloh...it's more nuanced than that. The ultimate answer to your question is always going to depend on who you are asking.

(If you think this helped, I can get into the more nitty-gritty tactical stuff. McClellan's career is an infinite rabbit hole of drama and second-guessing)

SOURCES:

• Adams, Michael C. C., and Stephen W. Sears. “Landscape Turned Red: The Battle of Antietam.” The Journal of Southern History, vol. 50, no. 3, 1984, p. 484., doi:10.2307/2208595.

• Army, Department of the. The Soldier's Guide: The Complete Guide to U.S. Army Traditions, Training, and Responsibilities. Skyhorse Publishing, Inc., 2017.

• Bailey, Ronald H. The Bloodiest Day: the Battle of Antietam. Time-Life Books, 1993.

• Carman, Ezra, and Thomas Clemens. The Maryland Campaign of September 1862 Volume II, Antietam. Savas Beatie, 2012.

• Sears, Stephen W. Landscape Turned Red: the Battle of Antietam. Houghton Mifflin Co., 2003.

• “Stare Down; or, Was Antietam a Draw and Was George McClellan Really in Charge?” Encyclopedia Virginia, The Blog, 18 May 2012, www.evblog.virginiahumanities.org/2012/05/stare-down-or-was-the-antietam-a-draw-and-was-george-mcclellan-really-in-charge/.

** Ezra Carman actually fought at Antietam, as the Colonel of the 13th New Jersey Volunteer Infantry. They were part of the XII Corps, which meant that his day was very similar to this scene from the movie Glory. Carman's regiment was in the same brigade as Robert Gould Shaw's 2nd Massachusetts. Realistically, you could substitute Carman in place of Shaw in this scene and it'd still be incredibly accurate.

(for the record, I agree with you. Antietam was a stunning victory in many ways that didn't make much sense at the time. McClellan was always great at seeing the "big picture" that everyone else missed. The only other people that truly, completely realized the absolute horror of the Civil War and what it would actually take to win it were Grant, Sherman, and probably Nathan Bedford Forrest.)