Thanks for coming here to raise the issue, share your perspective, and ask how to improve your question. I'll share my personal perspective (with the understanding that others might not agree with it).
I'm inclined to agree with closure of that question in its current form. I'd prefer to see this site for focused questions that admit an objective answer -- or at least where it is possible to objectively evaluate proposed answers -- as I think that's where the site format works best. This means that the question needs to define the requirements or criteria that should be used for evaluating answers. Answerers need that information so they can tell what would count as a satisfactory answer for you, and voters need that so they can tell which answers to upvote.
Right now the question feels like it has the form "please give me a list of possible distance metrics; I'm not telling you how I will evaluate them, but please give me a list so that I can choose one, using criteria that I haven't listed in the question". I don't think that's a good fit here. We want you to think through what your requirements or criteria are before asking and articulate them in the question. Sometimes a helpful way to do that is to come up with some possible metrics on your own, see if you're happy with any of them, and if not, think about why you've rejected them and what requirements/criteria that implies you have.
There tends to be some skepticism about "list of X" questions, because they are so open-ended. In particular, there is an infinite number of possible distance metrics, with no clear way provided in the question to select among them. No answers could reasonably enumerate all possible distance metrics, and that's a hint that the question isn't focused enough. It's also unfair to answerers: it asks them to spend a lot of time typing out many candidate metrics, most of which you are going to reject. Since you're asking for help and time from others, I think it makes more sense for you to first figure out how you plan to choose among the candidates, and make that clear in the question.
I do see that you provide some criteria in the question: "easy to compute on graphs of size 10", "invariant to permutations of nodes". That's helpful. Unfortunately, as the comments indicate, these aren't enough to narrow things down sufficiently yet: there are still an unbounded number of distance metrics. As David Richerby explains, essentially everything is easy to compute when the graphs has size 10, so that doesn't really narrow things down. And "invariant with respect to relabelling of nodes" is in some sense part of the definition of a graph metric. It's good that you include it, but it also doesn't narrow things down to a small list of possible answers.
So, this doesn't mean that your question can't work here. It just means we need more information before the question is answerable. It means that if you'd like the question to be open here, you should edit the question to clarify. What do you want the distance metric to measure? How will you evaluate a proposal?
Please don't view the responses as hostility. I don't see it as being hostile or aggressive towards you, personally. Rather, it's addressing the substance of your question: it looks to me like people are trying to keep question quality high and make sure questions are suitable for our site's format, and gather the information they'd need to give a good answer.
If you do see comments that violate our be nice policy, please flag them for moderator attention. Don't engage -- just flag them and move on.