Nope. My first girlfirend's father had a life-long schizophrenia triggered with a short series of binge drinking when he was 18 (!!!) and never touched weed or anything else.
Case point 1 but simple fact is, tons of people have some sort of predisposition to some form of mental illness. Wife is a doctor and she nicely sums it up - its not binary, tons of folks having miserable life are in scale 1-10 somewhere in lower part of one or the other mental illness (or more). Bipolar, OCD, ADHD, schizophrenia, etc., you name it. She deals with them daily.
For some, weed could trigger it. For some, some other drug or some big shock (close relative death, accident, violent crime etc). Since we don't ban the rest, banning the weed is just cargo culting due to US policies re hippies from Nixon era, enforced globally due to UN treaties. Which led to ridiculous situations where places like India or Nepal having marihuana as holy flower of god Shiva for literally thousands of years, using it to celebrate him, and suddenly had to ban it... at least on paper. Because bureaucracy.
Your father is not a good reference for this topic, its often a sad story when such people are asked to make policies that govern us all. They are always 'too deep' in the problem, see only the worst cases, so inevitably for them its the source of all evil and extremely dangerous. They don't know how happy, connected with nature and universe one can feel, how sex can be 10x better than best one he ever had, and orgasm can be literal nuke in your cranium, by far the strongest experience in ones life. Or tons of other, positive effects if not used in excess.
Ask doctors who work on alcohol rehab clinics whether it should be banned. Most will say definitely, and those who don't simply because they use it to self-medicate depression. And that is only because its socially acceptable drug, although way more destructive than weed could ever be.