Because the U.S. government never recognized the Confederacy as a separate legal entity. The "Union" isn't just a cute nickname. It's a reference to the preamble of the U.S. Constitution:

We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America.

The "more perfect" part is in reference to the U.S. Constitution being a replacement to the U.S.'s previous basis of government, the less perfect Articles of Confederation, which is properly called in full the "Articles of Confederation and Perpetual Union". That document started:

To all to whom these Presents shall come, we, the undersigned Delegates of the States affixed to our Names send greeting. Whereas the Delegates of the United States of America in Congress assembled did on the fifteenth day of November in the year of our Lord One Thousand Seven Hundred and Seventy seven, and in the Second Year of the Independence of America agree to certain articles of Confederation and perpetual Union between the States of Newhampshire, Massachusetts-bay, Rhodeisland and Providence Plantations, Connecticut, New York, New Jersey, Pennsylvania, Delaware, Maryland, Virginia, North Carolina, South Carolina, and Georgia in the Words following, viz. "Articles of Confederation and perpetual Union between the States of Newhampshire, Massachusetts-bay, Rhodeisland and Providence Plantations, Connecticut, New York, New Jersey, Pennsylvania, Delaware, Maryland, Virginia, North Carolina, South Carolina, and Georgia."

So when the U.S. Constitution says it is forming "a more perfect Union," it is specifically saying that it is replacing the imperfect "perpetual Union" formed by the Articles of Confederation with a better one. And since this is a "perpetual Union," the only way to exit that union is by the means outlined in the U.S. Constitution, that is, a state needed to get an Amendment passed by a vote of 2/3 of both Houses of Congress and 3/4 of the state legislatures in order to be allowed to leave. Short of that, the Union was perpetual, and the Southern states had no legal basis to disobey the Constitution and fight against its own legal federal government.

In other words, the Confederate viewpoint was that they were two separate countries now and they were fighting to uphold their recently declared sovereignty. The Union viewpoint is that the Constitution was still the legal governing document over all the states, that secession was illegal under that document, and they were fighting to preserve that document which was the legal framework for U.S. government and had been since 1787 when all the states had ratified it. And when new states had been admitted to the Union later on, they were also legally bound perpetually under the document to recognize the U.S. Constitution as their basis of government.

Ulysses S. Grant succinctly summed up the legal position of the U.S. government and popular sentiment when he wrote a letter to his father on April 21, 1861, the week after the Confederates had opened fire on the U.S. Army at Fort Sumter in South Carolina:

Whatever may have been my political opinions before, I have but one sentiment now. That is, we have a Government, and laws and a flag, and they must all be sustained. There are but two parties now, traitors and patriots and I want hereafter to be ranked with the latter, and I trust, the stronger party.

The Lincoln government, and the citizens of the North, never recognized the Confederacy as a "foreign and hostile state". They recognized them as fellow U.S. citizens who had engaged in an illegal act, an illegal war, against their own government, and were traitors to that government. Thus, those remaining loyal to the U.S. Constitution referred to themselves as part of the "Union", preservers of the U.S. Constitution and the union of states as referred to in the Constitution's Preamble. The Conferderates were traitors, by the U.S. Constitution's definition, and were in open rebellion against their own country's legal framework, and were acting illegally.

For more information on the lack of legal basis for secession and the South illegally waging war against the U.S. government and its armed forces:

The Concept of a Perpetual Union by Kenneth M. Stampp, 1978

Justice in Blue and Gray: A Legal History of the Civil War by Stephen C. Neff, 2010

Constitutionalism in the Approach and Aftermath of the Civil War by Paul D. Moreno, 2013

The Self-inflicted Wound: Southern Politics in the Nineteenth Century by Robert Franklin Durden, 1985

The constitutional history of the United States by Francis Newton Thorpe, 1901

Changes in Law and Society During the Civil War and Reconstruction by Christian G. Samito, 2006