A problem with the rebranding of Favorite as Like are all the historical favorites we've created, and the symbol that Twitter has chosen for Like. 

On Facebook, there is no Heart for liking. They use a thumb-up. A lot of thought must have gone into this. We like things we don't actually like, and shrug off the confusion. But labeling it with a red heart pushes it further. 

Example: You may have Favorited something about a terrorist group, but would you have clicked on a red heart? At the very least that's going to take some getting used to.