My seagate external drive will not format

Have you tried formatting it with Recovery HD or Internet Recovery? The one thing to make sure with those is that Show Only Volumes is the default, so you would need to select Show All Devices.

Give this a try:

Drive Partition and Format - El Capitan or Later

1. Open Disk Utility in the Utilities' folder.
2. After Disk Utility loads select the Seagate BUP drive (out-dented entry with the mfgr.'s ID and size) from the side list.
3. Click on the Erase tab in the Disk Utility toolbar. A panel should drop down.
4. In the drop down panel set the partition scheme to GUID. Set the Format type to APFS (SSDs only) or Mac OS Extended (Journaled.)
5. Click on the Apply button and click on the Done button when it is activated.
6. Quit Disk Utility.

If it fails keep trying. Sometimes it can take several attempts. If you still cannot succeed then try this:

1. Restart the computer. Immediately after the chime hold down the CommandandRkeys until the Apple logo appears. When the Utility Menu appears:
2. Select Disk Utility from the Utility Menu and click on Continue button.
3. When Disk Utility loads select the Seagate BUP drive (out-dented entry) from the Device list.
4. Click on the Erase icon in Disk Utility's main window. A panel will drop down.
5. Set the Format type toMac OS Extended (Journaled.)
6. Click on the Apply button, then wait for the Done button to activate and click on it.
7. Quit Disk Utility and return to the Utility Menu.
8. Reboot normally.

If the disk still will not unmount then quit Disk Utility. Select Terminal from the Utilities’ menu in the menubar. At the Terminal prompt enter the following:

diskutil unmountDisk force /dev/disk2

Press RETURN. The above command line is case-sensitive so be sure to enter it as typed above. If the command does not fail then quit Terminal. Select Disk Utility from Utility Menu and click on the Continue button.

1. When Disk Utility loads select the Seagate BUP drive (ghosted entry) from the Device list.
2. Click on the Erase icon in Disk Utility's main window. A panel will drop down.
3. Set the Format type to Mac OS Extended (Journaled.)
4. Click on the Apply button, then wait for the Done button to activate and click on it.
5. Quit Disk Utility and return to the Utility Menu.
6. Reboot normally.

One of the above should get the drive formatted properly. I suspect that the drive is pre-formatted for NTFS which is read-only for OS X. Reformatting an NTFS formatted disk can sometimes be a problem for Disk Utility.