Columbus was a product of his times
"Columbus was a product of his times. Sure he did some terrible things like have thousands of native Americans killed, raped, mutilated, and enslaved, but slavery was the norm then! The Mayans and Aztecs did the same things! Why single Columbus out as a bad guy?"
Yup: Columbus was a product of his times. He grew up in a time and place where slavery was normal, and rape and pillage were the literal God-given right of the conquerors. It's no big leap to imagine that most people at the time felt the same way. And the non-Europeans were doing the same things. Africans were enslaving and slaughtering Africans, the Native Americans were enslaving and slaughtering Native Americans, and the Asians were enslaving and slaughtering Asians.
Fast-forward a few hundred years, and even our own "founding fathers" owned slaves and thought very poorly of the Native Americans, often ordering many atrocities. But we still have holidays honoring them!
The moral of the story is that it's tough to judge people from hundreds of years ago by modern standards, I guess.
So, I guess that means Columbus Day is OK?
George Washington and Thomas Jefferson, for example, may have done terrible things, but we don't honor them for those terrible things. They had higher ideals like forming a representative government and freedom and liberty, and, although they were highly inconsistent in the implementation, we still believe in those ideals today. They were our were our presidents, and they owned slaves. They are honored for having those higher ideals and helping found our country. They are not honored for owning slaves.
Columbus sailed the ocean blue to seek gold and fame, and to get a better deal on spices. End of higher ideals.When he landed in the Americas, he immediately killed and enslaved natives in his pursuit of gold. Over his several voyages, he and his troops enacted a brutal regime to gain land, gold, and slaves. Simple profit and power were his "higher ideals", and he did not have any moral apprehensions about the means of achieving them. 
I've heard we should honor Columbus because was a great navigator, but that sounds really… strange, doesn't it? Do we have federal holidays honoring really good engineers or railroad workers or authors or any other occupation? No? I guess if we squint funny, I could say "the Presidents" and "the Veterans". And a very specific navigator named Columbus. Seems weird.
Besides, it's not really true. He ignored the mathematicians and cartographers of his day who gave him a somewhat accurate size of the earth, and instead substituted in a few verses of the bible and other ancient sources and thought it'd be a short trip across the ocean to India and China. If fact, if the Americas weren't there (as he believed they weren't), he'd have had to have gone approximately 12,000 miles instead of 3,000 to actually reach Asia that way, and he'd surely have died or needed to turn back. So it was blind luck that saved him from his own poor navigation.
The most that can be said is that he was eventually successful at convincing a monarch to fund his wacky "Sail West To Get Eastern Spices" start-up idea.
The other arguments I've heard for keeping it a national holiday make little sense either, most of which seem to boil down to "We've always celebrated it" and "He was good at monetizing the trips", which seems hardly adequate to justify a national holiday.
Though I'm not big on "celebrating" Presidents' Day, I understand why people could want it, in spite of the negative things the first presidents did. But for Columbus Day, I'm at a loss. The main reason people seem to want to keep it appears to be because they hate the "politically correctness" of recognizing it is a terrible holiday.
I'm all for requiring holidays to justify their own existence… So, Columbus Day: why should we keep you?