“Forwarding” here almost certainly refers to the From: header in the email. If I receive an email at my personal gmail address with “From: noreply @mybank.com” that was sent to me by “myuniversity.edu”, gmail will start to mark that email as nondeliverable because the message “claims” to come from the bank. But this might be a normal setup. Perhaps my bank has my university email address, and my university mail server is configured to pass the email along.

Clicking the forward button merely copies the email body into a new message appearing to come “From:” your personal email address, so there isn’t an issue with that. Doing this doesn’t preserve headers however.