Antonyms for the phrase "tying up with" would include words that convey the opposite meaning - a separation, a disconnect, a disagreement, or a lack of cooperation. Words like detach, disconnect, disengage, loosen, release, separate, sever, and unfasten come to mind. The concept of antonyms is important in language and communication as it helps us to understand the full range of meanings and nuances of a word or phrase. By exploring different antonyms for "tying up with," we can better appreciate the complexity of relationships and the dynamics of collaboration, partnership, and teamwork.