Not able to delete the standard user on mac air

You must first click the padlock on the lower left corner of the System Preferences window to unlock the System Preferences before you can use the "-" icon to delete a user.

Delete a user or group on Mac - Apple Support

Never mind -- it just took a long while to work and get to the next stage about deleting the home folder, but eventually it worked.

I have the same question, except it's about an iMac running High Sierra that I am about to give away. I unlock the padlock, but when I click on the unwanted user (me -- now a standard user rather than admin), and click on the minus key, nothing happens. I have made the recipient of the computer the new admin and have logged in as that administrator.

Here is what you should do when selling a Mac:

What to do before you sell, give away, or trade in your Mac - Apple Support

If your Mac uses a hard drive (as opposed to just using an SSD), then I recommend first enabling Filevault and letting the encryption process finish before performing the clean install which is the last step in the above linked article. Unfortunately Apple's instructions for a clean install just assumes users are only using an SSD or their Macs are encrypted using Filevault. When using Disk Utility to erase the Mac you may need to click "View" within Disk Utility and selecting "Show All Devices". Select the physical drive (or if using a Fusion Drive, then select the "Fusion Drive" item) and erase it as GUID partition and MacOS Extended (Journaled). With this modification to the instructions there is no need to unlock the Filevault when erasing the drive. Then continue with Apple's instructions for re-installing macOS.