Most internet communication is now end-end encrypted using TLS. In the TLS process, the TLS server sends a PKI certificate to the user which then gets authenticated using the CA's root certificate that it has (I believe it's stored in the browser).
Compromising the certificate store on the user's machine and installing a fake CA certificate means you can intercept traffic. But, how is this possible? In normal operation, I assume, the CA's public key is used to verify the CA's private key was used to issue the TLS server's certificate. The fake CA certificate would have a false key pair, so how does the authentication proceed?
I feel like there is a big gap in my understanding of this. I would appreciate corrections and insights.