We refuse to give that part of ourselves?

"we refuse to give that part of ourselves"? "we refuse to give (what to) that part of ourselves"?

Context:

Men who as boys felt neglected by their dads often remain distant from their own children. The sins of fathers are passed on to children, often through the dynamic of self-protection. It hurts to be neglected, and it creates questions about our value to others. So to avoid feeling the sting of further rejection, we refuse to give that part of ourselves we fear might once again be received with indifference. When our approach to life revolves around discipline, commitment, and knowledge [which the Greek influence teaches us] but runs from feeling the hurt of unmet longings that come from a lack of deeper relationships, then our efforts to love will be marked more by required action than by liberating passion. We will be known as reliable, but not involved. Honest friends will report that they enjoy being with us, but have trouble feeling close. Even our best friends (including spouses) will feel guarded around us, a little tense and vaguely distant. It\'s not uncommon for Christian leaders to have no real friends. [Larry Crabb, Inside Out (Colorado Springs, Colorado: Navpress, n.d.), 98-99.]