The Union never invaded the South - a country cannot invade its own sovereign territory by definition.
But the so-called Confederacy did invade territory that, by its own admission, it had no sovereign jurisdiction over. Namely Pennsylvania.
The Confederacy also invaded, at different times, Kansas, Missouri, Ohio, Maryland, Kentucky, Indiana, Ohio and West Virginia.
To be fair, the Confederacy claimed KY, MO, MD and KY as part of the CSA. And they, quite ironically, denied the right of WV to secede from VA. But Ohio, Indiana and Kansas were indisputably foreign territory.
Confederate agents also raided Vermont from Canada.
Denial of facts do not change the facts, in other words, just because Lincoln said that the South couldn't secede doesn't mean that they didn't secede.
But the so-called Confederacy did invade territory that, by its own admission, it had no sovereign jurisdiction over. Namely Pennsylvania.
That's called War; a war that was brought on by disHonest Abe for political purposes. I'm sure that you know that the stratagem behind Lee's invasion was to bring an end to Lincoln's illegal war.
What do you mean by the "so-called Confederacy"? Is this another example of denial?