Adobe Reader and Adobe Acrobat let you print double-sided if your printer supports that feature. The printer driver controls the options, not Adobe Acrobat or Adobe Reader. Check your printer documentation to see what features your printer supports. (Double-sided printing is also called duplex, back to back, front and back, or two-sided printing.)
Currently, the print settings in macOS take precedence over the print settings in Acrobat or Acrobat Reader. When you try to print double-sided in Acrobat or Acrobat Reader, the printer does not print as per the specified settings in Acrobat/Reader. Therefore, you have to configure the print settings using the CUPS admin interface in Mac.
CUPS (formerly known as Common UNIX Printing System) is a network printing service used by Mac computers. It allows you to set up your printers on a network, and customize printer options. By default, the CUPS web interface is disabled on Mac.
The settings specified in the CUPS interface overrides the print settings in Acrobat or Acrobat Reader.
Make a selection from the Print On Both Sides pane. Depending on the printer driver, this pane can be called "Double-sided printing" or a similar name. If you don't see a Print on Both Sides pane, then your selected printer doesn’t support duplex printing. Or, the feature is turned off (see Verify that printer features are turned on).
If your printer doesn't support double-sided printing, you can manually print your document using both sides of the paper. The steps vary depending on the way the printer feeds and outputs the pages. Print a few test pages following the instructions to understand how to feed the pages back into the printer.
Follow these instructions if the printer outputs the pages in numerical order (starting with page one). The pages exit the printer face down (common with laser printers).
Follow these instructions if the printer outputs the pages in reverse order (last page first). The pages exit the printer face up (common with inkjet printers).