From their very first meeting, undeniable chemistry arose between the two
As Cooper finishes ordering breakfast with a request of some grapefruit juice, he glances over at the young, alluring Audrey walking towards him. Cooper fixes his eyes on her and, completing his order, says “just as long as those grapefruits are freshly squeezed”
Dale does not want to allow a romantic relationship with Audrey. First, he wants to fulfill his moral duty as an FBI agent by not getting involved with someone so closely connected to the case
Secondly, he must fulfill his duty to the much younger Audrey as her protector, and more importantly, as her friend. He also later reveals that he failed to save his last romantic partner from danger to his career, resulting in her death. It's clear that he doesn't want the same thing to happen to Audrey