The announcer for the football game just mentioned that one of the players is favoring his injured shoulder. My husband commented that one would imagine he would favor the one that didn't hurt, as it would be more useful during the game.
That got us onto the subject of words that are their own opposites, such as "favor", which can mean to not use because of injury (i.e., a body part), or to prefer. Those aren't exactly opposites, but pretty close in the circumstance of, say, an injured football player.
The only other two we could come with right away were "inflammable" and "cleave". There may be others, but even just those three provide good examples of why English is such a challenging language.