Hmmmm I've been on all sides of this fence I think. I totally get that some people are more than happy not marrying but fundamentally marriage is important to me.
I used to say it was just a piece of paper and that my exDH and I had a house together so it didn't mean anything. But we were young (too young) and getting married was kinda what you did next so we did. I refused to change my name as I felt very strongly about my identity. Weddings don't interest me at all so it was a small surprise ceremony. Being married was actually kind of different. Hard to put a finger on exactly how but it did feel more serious, bonded, connected in formal ways. Anyway we got divorced 3 years in. Some might think I'm hypocritical saying marriage is important and being divorced but that's life.
After my divorce I didn't think I'd get married again, certainly not so soon (I was married again 5.5 years after I got divorced) after being with DH for less than 2 years. When I met DH he was totally against marriage and kids. Which didn't bother me as I had already been married (no kids though). So we bought a house together and got serious. And then we got married just us on a beach. He felt that he wanted that stability and commitment and tradition (where did that come from?!) and so did i. I even changed my name this time as I wanted us to be joined in that way. Lo and behold we've been married 4 years now and have a 6 month old DD (my DH has changed a lot over the past few years all on his own volition, we grew into these decisions together). It's lovely.
Again this time it does feel different. My DH used to say it's nothing more than a piece of paper, he's quite non-traditional and we're both not religious. He does feel very strongly that it's different both on paper and in spirit I guess which surprises him. Yes you can still walk away and relatively easily end a marriage but it is formalising a relationship in a legal sense. Many people place no stock in that and that's cool but I guess I'm old-fashioned in that I like being married I can't wait til our best friends (SS) can tie the knot.
OP if it means a lot to you what is the impasse from DP? He obviously feels very strongly against it. It is sad where there is such an imbalance of feeling. Sometimes as a PP said if one person cares less about their position they will go with what their partner wants. Sounds like you both are at opposite ends of the spectrum. I guess you both need to look at what is important and why and whether the symbolism of that is damaging the core of your relationship. It's one of those things you can't push or force.
My heart goes out to you as I can sense a deep sadness from your post x