Is it really such a bad thing to have an undefined relationship

We're both fully exclusive, we have defined the relationship to be that we are together, we are in a relationship, we just don't say that we're gf and bf. Everything but the label applies.
If anyone asks, we do say "I'm with someone".

My friend thinks it's a red flag that he wants to keep it this way, but he treats me so well that it sometimes surprises me, he always reassures me when I'm insecure or anxious about our relationship, he's so respectful of me and my boundaries. This is the only slightly strange thing he's asked of us yet, and I didn't find it alarming until she brought up the other side of this.
We're both just starting to go into college, he's going to study medicine and I'm going for architecture, both very demanding courses where we may not be able to put in as much as a conventional relationship demands.
He's scared that by labelling it, it's much easier to break. This way, it's easier for us to take a break from the relationship and have a friendship to fall back on to fix whatever it is that made us take a break.
But my friend is scared that this way, he'll always have access to me to contact me even when we're done.
But that just depends on how I choose to leave this, right?
Is it really that messed up or is she playing devil's advocate and causing me to over think this...?

"He's scared that by labelling it, it's much easier to break. This way, it's easier for us to take a break from the relationship and have a friendship to fall back on to fix whatever it is that made us take a break."
That's a contradiction, unless you meant the first sentence to end with 'break up'? If so, that is a concern. If you need to sort out a issue in a relationship, why would you not stay together and do that? There's no guarantee you'd stay friends, and to me, to think like that is showing a lack of commitment and that things would be allowed to drift along. This is coming from someone who has experienced demands of 'both being in the Armed Forces, still in an LDR' relationship.
As an aside, how you are introducing this guy to people; 'I'm in a relationship and this is who I'm with'? Why not bf/gf?

When I say that it's easier to break, I mean that it's an "all or nothing" situation, which would always be on the edge when we have a rough patch. We're pretty young now and this is both our first relationship, it is going to be tricky to navigate, especially when we're trying to set up our own lives
And as for introducing eachother to people, we live in a country where it would not be okay for us to have a relationship. We would never actually be able to publicise a relationship until we're like 25 (which is more than 5 years away, at which point we may not even be in contact). Our friends already know that we're together, but that's as far as the publicity of the relationship will go...

The second paragraph I understand, but not the first. You are both adults and have chosen to be in a relationship where yes, things may not always run smoothly, but why would it be 'all or nothing'? Don't you want to stay together; leave it's unreasonable, otherwise you discuss, you compromise, you support each other.

Right now, we're 17 and 18 (with barely a few months of age difference between us),we finished 12th grade a month ago. We don't even know where we'll be 2 months from now.
We are together, that's a certainty, but I also see that where he's coming from is not from a place of toxicity, but of uncertainty about where our lives will go.
We're literally trying to start life right now, and by committing so hard at a time where we're transitioning from being unable to support ourselves to being completely independent, it seems like it would be difficult to separate that. We can't be building our lives around a place that could be empty tomorrow. Yes, we both want this to be a long term relationship, but realistically, we don't know the kind of adults we're going to turn out to be, we don't know the kind of lifestyles we're going to have to live, it eventually may not be compatible.
When I say "all or nothing", I mean that if we see that something about who we are in that period of time isn't working for the relationship, and we end up breaking up, cutting contact and moving on, there's no going back.
But this way, we can take time off to see that this is just a small change that with time, will work it's way out and we are still good for eachother, it was just us trying to find our footing. We would have a friendship to fall back on, where we still have the support of eachother, but we don't need to deal with something that as a gf/bf, would be unfair to deal with.
Obviously, the issue would have to be something that doesn't break the fundamentals of the relationship like cheating or dishonesty. It may just be a small thing like lifestyle choices, stress, bad peer influence. Stuff that we'll eventually see sense in, but could cause unhealthy tension in the relationship
(I'm so sorry, I'm typing way too much)