How you say 'No' determines a large part of your success as Product Owner
How you say 'No' as a Product Owner is important.
Saying no is the easy part.
Saying no while preserving the relationship is hard. Nobody likes to hear no. It can get personal quickly.
You need to be able to carefully weigh your words and pick the right ones for your situation by reading the room. You need to be able to deliver those words with the appropriate tonality and body language to minimize your chances of offending others.
It's not just what you say but how you say it.
Saying no while preserving the relationship and making them understand the reasoning behind your decision is even more difficult. Clarity of thought and clear communication is essential. You need to carefully articulate your reasoning through the lens of the product vision.
Do it right and you will rarely have to say no.