Is it normal to CC my professor when they introduced me to someone?

Most faculty are curious and would like to know what their students are doing, therefore you should CC them. If you CC them, they don't have to ask you if you sent the email. If you CC them, they have the opportunity to clarify what you have written.

Some faculty consider deleting an email to be an unpleasant chore. If your supervisor is one of those people, do not CC them.

Otherwise it is a matter of individual preference. Few people consider it rude to CC or rude to not CC.

As a professor, I suspect it's fair to say that there is no "norm" about this (in my culture at least). Both your professors' remarks are reasonable ways to think about being cc:ed on an email.

When in doubt, I recommend doing the cc:ing, after comparing the potential downsides: needing to delete one email (several seconds of thought), vs. being unsure about how one's student is doing (a more lasting mental state).

I think there is no norm. I can understand both positions, as

a) I don't like to be included as recipient of many emails, as I don't like to follow every detail but want to get an overview. So I'd like to be informed in weekly meetings.

b) When I forward the contact of a friend or an old contact, which I value, I don't want that a student messes up with inadequate questions or at worst rude requests.

People tend more towards a) or b), also depending on the topic. You need to find out what to do depending on the topic and the professors you interact with.
As you know now that it is a deliberate topic, ask next time whether the professors wants to be included. From that you can derive if you need to include your professor for less controversial topics.