Very fair point. I would say there is definitely a fine line there.
But being proud is certainly not arrogant.
The key takeaway is learning to be proud of your own work – this does not necessarily mean deciding it’s better than everyone else’s, but just believing in what you bring to the table. Clients want to hear what you have to offer so don’t be shy to show off what you have done. Confidence in your own ability and work is essential – but I would avoid assuming your work ahead of everyone else’s. That is where the arrogance lies.
Everyone brings different styles and methods that can be suitable to different projects, so count yourself among them, rather than above.