The reason for disliking them is that they permit "less structured" control flow.
GOTO permits totally-unstructured control flow. break and continue are like a restricted form of GOTO.
Structured control flow is preferred because it is easier to correctly understand it when you read it. Remember, the next person who will read the code that you write will be a violent psychopath who knows where you live.
Consider reading Djikstra's "GOTO considered harmful" paper. I don't know if you'll really understand it, but try.
In my opinion, when you consider writing break or continue your should ask yourself "How could I write this otherwise, and would that be more or less clear?". If the alternative would be less clear (to the axe-wielding psychopath), then break and continue are fine.