That's a lousy answer. Tape *does* work. It can be slower than disk, but disk is not the *only* way to have a usable backup. Tape is not dead.
Tape works. Disk works. Offsite replication works. Do the math for how much data you have and how much bandwidth you have or can afford, and do the calculations on how much data you really have to back up. In many cases, recreating the data can be significantly cheaper than backup it up and restoring it. If you have your original CDs and DVDs, put them in an offsite location. If you have a disaster, you can have them re-ripped for a LOT cheaper than backing them up.
I've help run a multi-petabyte data center with backups to tape and they worked. Everything written to tape was restorable. I currently run a multi-petabyte data center and replicate everything to disk in an offsite location. It also works. Neither is cheap.
Figure out what part of the data is important to you and how long you can wait to get it back. If a fire burns down your house but you need the data back in minutes or hours, then tape is obviously not the answer but then neither is DVDs or any cloud provider.
There is NO single answer that's good for everybody. It's a cost/benefit/risk analysis that every first year comp sci student better become familiar with.