A tendency.. Seemingly. Prove isn’t even the best word here. His theories are not well accepted.
For example, he talked about a patient he had that dreamt about a beetle. When his patient was telling him the dream, a beetle started tapping on his window. He used experiences like this to claim that we are all connected in some way. And maybe that’s true but this isn’t indisputable proof. Jung practiced as a therapist for over 50 years. Do you understand how many patients he had to have seen in that time span? Most likely thousands. It’s not a stretch to say that this beetle story was just a coincidence. It’s certainly a stretch to claim that this coincidence is somehow special when the rest of his work with his patients were very ordinary. In order to prove something, you have to show a consistent cause and effect relationship. Do insects tap on your window whenever you dream about them? No they don’t.
A simpler example of these “meaningful coincidences” is when you dream about someone and find out that person also dreamt about you. It’s happened to me several times where I’ll text this person and say I dreamt about you. They’ve responded saying they also dreamt about me. Wow crazy must be proof of something right? Maybe not. How many times have you dreamt of someone who didn’t also dream about you or reach out to you? All the damn time. You just don’t notice. It’s a bias and it’s difficult for people to acknowledge that. Everyone thinks they’re special and immune to these biases but no one actually is. Not even Jung.