How do you strongly hold an opinion... but hold it loosely? I think it's a poorly worded phrase, but here's how I interpret it.
An opinion worth holding is one worth defending. Scientific experiments start with a hypothesis, an informed opinion. It's an opinion they believe is worth exploring. Otherwise, why bother and waste time for all parties? Many open source projects have an RFC process. Why bother submit one when you're willing to withdraw it at any feedback or criticism?
But for all of these processes, there needs to be a certain threshold for them to pass. How much supporting evidence is required to validate a hypothesis? How much support is required approve an RFC?
I believe this is where it gets fuzzy, and important. There is no clear answer for what that threshold is for each instance. It needs to be up to the owner of that opinion to decide at what point do they concede. The people that I've enjoyed working with the most excell at this. It's easy to hold constructive debates and maintain reason. We continuously help and challenge each other to improve. There's always a dance, a back-and-forth, some conflict, but a resolution at the end.
I think an opinion is kind of like story telling. There's something there, but it needs to be developed. I like Dan Harmon's Story Circle and it fits fairly well.
As you go through your career, what you really get out of your experience in the end is a collection of opinions -- "do this, do that", "this is bad", "this is good". And ultimately, it's your job to make sure that these are the "right" opinions to hold. So let's help ourselves improve and tread that fine line between maintaining your opinion and conceding to the other side.