Help reassure me I'm not losing it.

I'm turning right on this roundabout (green) and the blue car comes out at the same time causing me to nearly go into their side. They then start shouting at me that they have the right of way because they are on the straight part of the road. I was baffled, I've never heard this reasoning before. He was really cross and seemed adamant he was in the right. It's a roundabout tho! I'm not mad, am I?

I'm turning right on this roundabout (green) and the blue car comes out at the same time causing me to nearly go into their side. They then start shouting at me that they have the right of way because they are on the straight part of the road. I was baffled, I've never heard this reasoning before. He was really cross and seemed adamant he was in the right. It's a roundabout tho! I'm not mad, am I?