I remember being in college and hosting my own FTP servers on my old desktop in my dorm room. My FTP servers were a lifesaver when it came to being around campus and needing to access my school work where ever I was on campus. I remember many of my friends that wanted the same situation for their files so as a tech geek I would then SSH to my Linux box at that time a red hat dell desktop running raid 1 (the memories) in my room and create them an account using the useradd command as root.
You have to remember this is 2003 there are no jump drives yet and no portable hard drives at this point. You moved your files around using floppy disks and CDs. At that time in 2003/2004 that was considered the coolest thing in college that college tech guys could get their files anywhere and not have to worry about caring around CDs or floppy disks. This worked great as well for getting my MP3 that I used to play in Winamp around from PC to PC.
Now with the internet and cloud storage being what it is today no one needs to host their own FTP Server anyone except maybe large companies, but even that is becoming less and less. Anyone nowadays who buys Office 365 for 7 dollars a month has 1 TB of storage and every free Gmail account comes with 15 gig free storage.
Even better for users using a cloud storage like Dropbox, Google Drive, and OneDrive it takes little to no computer knowledge to set up and use. This is not the case when running your own FTP Servers.
The other issues with FTP Servers are why have to worry about user rights when you can just share the link to a file you want your friend to access via email like on Gmail. There is no worrying about giving friends or user’s access to your server and having to worry about managing username and passwords. Using cloud storage takes the risk away of usernames and passwords being compromised.
The other advantage of using cloud storage is a hardware failure. If your hard drive dies on your server you risk data loss whereas cloud storage has redundancy, clustering and off-site backups built to protect you from fires, theft and natural disaster.
As much fun as it can be to run your own FTP server and many companies and enthusiasts might still run their own FTP Servers but in the age of cloud storage, this is just not a feasible solution for file sharing. I would recommend cloud storage just from a safety and security standpoint over your own FTP Server unless you just want to learn.