Do I need a good argument for you to respect my opinion?

Not necessarily. If you have a lot of experience or a different perspective and you seem trustworthy to me, you don't need to have a good argument. On the other hand, if someone else comes along with a good argument why your opinion is wrong, I will start doubting you.

For example, if you've been growing potatoes for 30 years, you don't have to explain the biochemistry of potatoes for me to respect your advice. And if you're a black person telling me that our town is terribly racist, I will believe you without needing a list of every single racist incident that happened to you.