Our brains are incredibly sensitive to nuances and meta-messages - those very subtle "micro-inequities" or signals we send each other about who is up, and who is down - who has the power - who does not.
When we disagree with another person, we are stepping right into the dynamic "alpha-alpha" conflicts that set off people in the workplace, and sustain conflicts. Too often this dominates an organization leaving people feeling the are in a toxic, competitive environment.
Disagreeing with someone is not just "disagreeing with their point of view, or the information they are sharing. Disagreeing can communicate the following "meta-messages" if not careful:
1. I am right, you are wrong.
2. "You stupid idiot" (YSI) - how could you think such thoughts.
3. How could you see the world that way.
4. You must be blind to the truth
Human beings has a gene for "truth-telling" and when people disagree it is felt at the deepest level. We all want to trust our observations and beliefs, however disagreeing can challenge us at the core of who we are, not just and rarely just at the informational level.
Don't say, "yes - but" - and then deliver your perspective. The "but" negates anything that came before that appeared like an agreement - and turns the conversation into a combat.
Alternatively, saying "yes and" creates an extended conversation that builds on ideas - it says, what you said is really important, and lets take it one step further... the "and" invites further development of the conversation and expands perspectives. I call this type of conversation "co-creating" and when people in the workplace make a shift to this way of talking - even with they don't fully agree with others, it moves people away from adversarial behavior and into collegiality.
With a boss, using the phrase "respectfully speaking" is also a way of saying.... "I know I should respect your position" - "BUT" I don't' so here goes with what I think.
I understand what you are trying to say... help me with this aspect... I'm having trouble seeing how to get from here to there. This is an invitation to talk more deeply about beliefs or observations, it takes you out of the positional dialogue where you are going back and forth one-upping or arguing about what is right, and it invites people to be open to influence.
In summary, when we get into conversations that feel adversarial, we see people in "persuasion" using high levels of Advocating (their point of view). Sometimes they are Inquiring, however the intention behind it is to learn what the other person is thinking so you can turn the conversation back to "winning your point."
Sharing and Discovering
As an alternative, "agreements" come more easily when people are open to influence, and when we get into conversations that feel like partnering - where people share and discover from each other - open the context and framework to both gain new perspectives. Then agreements seem to be the outflow. Even if you agree to disagree - it comes with the spirit of respect.