The antonyms for the phrase "bringing pressure bear up on" are more relaxed and less pressuring actions. Some examples of antonyms would be to encourage, to support, to assist, or to facilitate. These words imply that there is no force or coercion involved in persuading someone to do something. Rather, the focus is on enabling and empowering the person to make their own choices. Offering choice, understanding, and a sympathetic ear could also be antonyms for the phrase "bringing pressure bear up on." By using these types of antonyms, one can create a more positive, collaborative environment that encourages growth and development rather than hindering it.