The antonyms for the phrase "looking over for" can vary depending on the context it is used in. Some possible antonyms include ignoring, neglecting, disregarding, forgetting, and overlooking. These words suggest a lack of attention or consideration, as opposed to the vigilant watching and assessment that "looking over for" implies. Other antonyms might focus on the idea of avoiding or circumventing instead of examining, such as evading, sidestepping, or dodging. In any case, the antonym chosen would likely suggest a very different attitude or approach toward the subject at hand.