Not entirely true in my experience. This would be particularly national interests and don't explain EU subsidies.

When staying particularly in Austria, the subsidies are there because national politicians and EU politicians from Austria want some part of the EU subsidies pot for their farmers, contributing to the general constant rope-pulling and trading "a piece of the cake" (i.e. EU budgets) - usually in the form of: "You get subsidies for x, we then get support for our poor farmers in poorer regions, since they are starving".

Generally the EU subsidies for agriculture are misguided and just money down the drain. Until they begin to dry up causing uproar and "EU took our money!"-complaints.

I think there might be some retroactive argumentation going on about why they exist which does not go back to the roots of it, but if you look at why and how the CAP was made and how subsidies and price fixing within the countries works, you can still see where it came from.