Liberalism did not eliminate slavery. The author of the United States’ Declaration of Independence, Thomas Jefferson, owned slaves on his plantation at Monticello. While Jefferson espoused the political philosophy of Liberalism, he, and many other powerful politicians, viewed their slaves as property and not people.
This was ingrained in the United States Supreme Court ruling on the case Dred Scott v. Sandford that declared slaves were protected property that the owner could use as they please – just like the rest of a person’s property.
The abolitionist movement eliminated slavery, not the political philosophy of Liberalism. It took the likes of William Lloyd Garrison, Frederick Douglas, Harriet Beecher Stowe, and John Brown to push liberals to eliminate slavery.