Survey after survey show managers and executives within companies who have people reporting to them want to know the truth from their employees. The same amount of surveys show that many employees do not feel safe sharing such truth with their superiors if they know the superior will disagree with it. The first step do doing so, according to communication experts, is to tilt the odds in your favor by picking the right time. Pick a time when the stakes are low and emotions are calm. In other words, not during a busy/stressful part of the workday. For those who are employed in workplaces where every day, all day, is busy/stressful, you may need to setup a time after-hours or come in a little early to catch your boss before the shift starts.
Another way to smooth the disagreement over is to not surprise your boss with it. Without going into it fully before your designated “low stakes/calm emotions” time frame, explain briefly why you want to chat. While giving that “intro” to the chat, wrap it in a frame of reference that the boss will appreciate/understand, such as the importance of accomplishing a goal or improving the bottom line. By doing this, you can reduce the likelihood the boss will misinterpret your intentions to something undesirable or confrontational.
One more thing that will help lay the groundwork for a successful disagreement is showing that you respect your boss and their decision. There is no exact playbook for doing this because everyone is different, but employees have reported success in this regard by properly underlying a positive rationale for why the boss may have made their decision, along with acknowledgement of their leadership in the process.