Speaking as an Evangelical and a non-denominational Christian, I think I can help you with the thought process that tends to happen. If you’re talking to someone like me, I am probably making some assumptions about why you question me so, and these assumptions may or may not be correct. But here is what they are.
Assumption one- you are asking me for a more specific label so that you can associate me with a particular group of Christians in a historical context. Once you do that, I somehow doubt that you are going to say a bunch of nice things about that group of Christians. I would probably tend to assume that you want to pigeonhole me and then find things to say about a particular group that are critical. I might even tell you I don’t like being pigeonholed, which I realize is a purely pejorative term and no one really goes up to someone with the goal of pigeonholing in their mind.
Assumption two- I might think of you as someone who is fishing for sectarian dirt. Or maybe I don’t even know that much about sectarianism. I remember when I was still in middle school, and I was participating in a broadly multi-church event for a particular charity. As I was mingling and talking with people, I started a conversation with a middle-aged man from another church, if he gave me any clues as to which one I can’t remember, and we sort of cut that part of the conversation short before we got there. I do remember that he asked me what sect I belonged to- “What sect are you a part of?” he said. And I remember saying “Ummmm, ahhh, it’s non-denominational, does that answer your question?” And he said, “No, I mean, what sect is it, sect- I’m sorry, maybe that’s a bad question.” And he kind of looked like he regretted getting into this with a kid as young as I was. So I said “No, wait, what did you mean by sect? I’ve heard the word but I haven’t really talked about it or broken down what it means for me.” And he basically said never mind, I just thought of something else we could be talking about, it means what branch of Christianity or maybe what part of Christianity broke off into another part but let’s quickly transition to a different topic.
That was kind of a long story, but it gets to a family of sect-related assumptions. First and foremost, it may be good to understand this- I did find out a lot more about sects and sectarianism as I got older, but not all non-denom people do that so much. When you ask a question that seems to be angled that way, that might be taking them into unfamiliar territory. They don’t know exactly what sects have to do with them, and they either don’t feel like they want to or have to. The second possibility is that they do know quite a bit about sects and sectarianism, but they are quite sure that the negative meaning tied to sectarian (a division resulting from conflict) has nothing to do with their particular church.
Additionally, if a line of denominational questioning turns sectarian in nature, it is probably good to familiarize yourself with the full range of what sect/sectarian can mean. Specifically, it can mean a narrow-minded and bigoted person, which tends to be the exact opposite of the mindset that a big-tent-Christianity non-denominational person tends to have. If that is the case (and it likely is), you may find that this person feels that they are being asked to define themselves on the basis of what they reject and disagree with instead of the thing that they generally like to do as a life goal- embrace all of Christianity and all Christians as much as they are able to do.
I hope this helps clarify one or two things, at least.