DiskUtility prompts file hard links wrong, can't be fixed permanently

1. Start up your computer in single-user mode to reach the command line.
   Note: If your computer is unresponsive, force it to power off by holding down the power button for several seconds. Then press the power button again to start up the computer.
   
2. At the command-line prompt type:
   

   /sbin/fsck -fy

   
   Press Return. fsck will go through five "phases" and then return information about your disk's use. Once it finishes, it'll display this message if no issue is found:
   

   ** The volume (name_of_volume) appears to be OK
   

   
   If fsck finds issues and alters, repairs, or fixes anything, it displays this message:
   

   ***** FILE SYSTEM WAS MODIFIED *****

   
   If this message appears, repeat the fsck command you typed in step 2 until fsck tells you that your volume appears to be OK (first-pass repairs may uncover additional issues, so this is a normal thing to do).
   
3. When fsck reports that your volume is OK, type

   reboot

   at the prompt and then press Return.

Your computer should start up normally and your disk has been repaired. If the "incorrect number of hard links" error persists remove homebrew, restart in single-user mode , and repair the disk with the fsck command you typed in step 2.

The fsck command checks and repairs inconsistencies in file systems. This is a known issue. There is a likelihood of finding some code in Homebrew and that code is causing this problem. It's likely that an otherwise valid operation is simply triggering a bug in something else. Multiple people say to be an issue with /Library/Formula/fish.rb

Remove homebrew, restart in single-user mode , and repair the disk

Is there any difference with your method and rebooting to recovery mode and fixing with disk utility?

No. The startup drive is failing, or there is some other internal hardware fault.

Back up all data on the drive immediately if you don't already have a current backup. There are ways to back up a computer that isn't fully functional—ask if you need guidance.

Make a "Genius" appointment at an Apple Store, or go to another authorized service provider.

If privacy is a concern, erase the data partition(s) with the option to write zeros* (do this only if you have at least two complete, independent backups, and you know how to restore to an empty drive from any of them.) Don’t erase the recovery partition, if present.

Keeping your confidential data secure during hardware repair

Apple also recommends that you deauthorize a device in the iTunes Store before having it serviced.

*An SSD doesn't need to be zeroed.