umbrage (UHM-brij), n.: suspicion of injury or wrong; offense; resentment
"However, as to his having called me a blockhead, it's not what I take umbrage at."
"A less kindly-tempered man would have taken umbrage at the tone of this letter."
From the Latin for "shade" (umbra), umbrage once had a literal meaning ("shade; shadow; foliage"), which is now obsolete. That a word meaning "shadow or foliage" could turn into one meaning "offense or resentment" is not really as unlikely as it might at first seem. The logic behind the change can be more readily understood with the help of an extended defintion: "umbrage: the feeling of being overshadowed; jealousy of another, as standing in one's light or way; hence, suspicion of injury or wrong; offense; resentment."
Umbrage is related to umbrella, which is Italian for "little shade," and which, etymologically at least, is properly for protection from the sun rather than the rain.