When it comes to disagreeing agreeably, it's all about tone. Tone is extremely important not just in our day-to-day conversations, but also in our writing. If we want to convey an understanding tone, then we should choose words that are simple and straightforward. The person we are speaking to should not feel attacked or threatened by our words, but instead feel heard and understood.
I will provide some examples.
In a conversation with someone you disagree with you might say, "I think that your idea is good, but let's think of some more that might apply to the situation."
That would be better than saying the following, "I disagree with your idea. Let's do this instead."
The second way completely negates the idea of the person, while the first way gives their idea credibility.
Do's:
"I didn't think of it that way. This is what I think."
"What an interesting idea! I want to share mine with you."
"Can you explain to me how you came to that conclusion?"
"That is one way to look at the situation. I see it this way."
Don'ts:
"I don't agree with you."
"I don't think that's what they meant by that."
"That's wrong."
"You're wrong."