Disk Utility cannot install macOS, so you're likely using Recovery or an installer of some sort.
I'm also assuming there hasn't been a hardware change here, and that the reason that this whole sequence is underway is not due to a hardware problem. Though failing hardware is usually possible.
For completeness, if Recovery isn't working for you, build a bootable installer on another Mac, transfer that bootable installer to the problem Mac and boot it.
Once Recovery or the bootable installer has been booted, use Disk Utility to erase and reformat the entire internal storage device to GPT, and then use Recovery or the bootable installer to reinstall macOS onto the internal storage.
Per MacTracker, all six of the 2011-era MacBook Pro models can run Mojave macOS 10.14, in addition to High Sierra macOS 10.13.
It's also possible that the storage hardware is failing, as that's one of the more common causes of folks looking to reformat their internal storage. Failing hard disk drives show as slow-downs, beachballs, crashes, and corruptions, among other symptoms. If this is a hard disk—the 2011 models were sold with either hard disks or SSDs—and if it's the hard disk that might be failing here—or if you just want some better performance and a few more years out of this MacBook Pro, an upgrade from a hard disk to an SSD can be a good investment. SSDs are vastly faster than hard disks, and a one terabyte SSD upgrade is about ~US$225. Options are available from various vendors, including from OWC. Which is where that price is from.