1) Fountain pens are far friendlier to the environment. You replace the ink, rather than replacing the entire pen. If you take care of your pen, it will last through generations. You can't say that about ballpoint filth.
2) Ballpoint filth uses friction to write. You have to press down to get the ball rolling into the paper to start the ink flowing. There isn't friction with fountain pens because the ink flows as soon as the nib makes contact with paper, so the nib flows over the paper rather than in it.
Why does that matter? Because the friction of writing with ballpoint filth makes writing painful, if not impossible, for people with hand pain issues such as arthritis, previous injuries to the fingers or hand, degenerative conditions, and even carpal tunnel.
Fountain pens also tend to come in larger barrel/grip sizes, which also helps with reducing hand pain still further when writing.
I am one of the people who has hand pain issues, and my doctor prescribed fountain pens for writing. It was the only way I could continue in college, and my professors have to accommodate my fountain pen use. I could not survive taking notes and writing assignments all day if I had to use ballpoint filth, or even gel or rollerball pens. Gel and rollerball sort of work better, but only by adding an hour to how long I can write with them. Fountain pens still allow me to write longer and with less stiffness or pain than any other kind of pen.
3) Fountain pens allow more flexibility with HOW you write. If you know what you're doing, then you can get most nibs to "spread" from pressing down on the nib, so that you can create considerable line variations in a way that ballpoints cannot offer.