I believe for many EU doubters this debate can't really be won on rational standpoints. Just because the EU funds stuff is not really at the core what these people care about. Its about nationalism and some kind of vague proud self sufficiency that is projected onto the past. As long as the EU is not an entity that people identify with, this will never change.
We need more directly elected institutions on the EU level and even stronger EU integration. The EU is necessary for Europe to stay relevant on an international level and be a chance at nation building without violence and coercion.