Was I in the wrong? Gym etiquette

So it’s 6 PM, peak hour gym, lot of machines occupied and it’s chest day.

I see a couple (i think) using a machine that i’d I also like to use so I walk up to them and I kindly ask them if I could hop in between their sets. The guy straight up tells me that I can’t because they immediatly go after eachothers set. I was kind of shocked, i did not expect no for an answer and what’s a 20-30 second pause if I hop in between them? I told him this is a public gym, you don’t this own place. He keeps repeating his answer and I keep repeating my answer and at this point it’s going nowhere, I could’ve done two sets during this argument 💀.

At this point i’m fuming, the guy was still not willing to let me and on top of it he told me you can get the gym staff if you want. I told him nah it’s alright we’re adults and I went to another machine.

Somehow i can’t let go of this event because i feel disrespected? For example, if anybody wanted to hop in between my set even if i was with a friend i would let them do their thing. Everybody has places go to and it’s a shared space.

Anyhow, was it wrong from my side to start an argument and should’ve just said aight bet and go to another machine after he said no?

Ngl the rage got me some extra strength during my workout so it was kind of worth it.