Is showing social media that your relationship is happy very important to you?

I'm tired of the bs painting a picture yet he won't understand. He accuses me of being "scared to show him off" because I don't post about him on social.

First of all, I don't use social. Second, logically I don't post if I don't use it. I tried to explain to him that I don't care but he keeps saying it makes no sense and that I just don't care. Wtf do I do? Help.

I had two pictures on my social (ig) . One about having ice cream with my brother (just the pic of ice cream and our hands) and another about a 3 year old pic of graduation day with my SO. I deleted both of them. Deleted my profile picture. And proceeded to delete the app. This happened at the beginning of the year. He just found out I did this yesterday. He is accusing me of hiding our relationship because I don't post his face. We have been together for 2 years.

It's always fights about social media and I'm SICK and TIRED of it. Advice is needed. We are 20 and 19.