> How is that giving medical advice? that's a mission statement.

As a mission statement for a software project, it very clearly indicates an intent to have the software act as a doctor.

> If my mission statement is to provide everyone with a private lawyer, then is that giving lawful advice?

If you have a software project with that as your mission statement, then its a pretty good indication you are aiming at unlicensed practice of law (which involves “legal advice” but exactly not, despite “legal” and “lawful” in other circumstances being synonymous, “lawful advice”.)