You get no proof for open source software either unless you perform a formal verification. And even then your proof may be wrong. But maybe we can agree on the

You get no proof for open source software either unless you perform a formal verification. And even then your proof may be wrong. But maybe we can agree on the following. Closed source software can be secure but there is a broad spectrum of needs for convincing someone that a software is secure and this need may be better served with open source software in some circumstances. For some it is sufficient to trust a vendor. Some want to audit the source code (and this does not exclude closed source software). Some even need formal verification maybe even of the underlying hardware.