Hello, according to that you are a new Mac user.
First, you have to know that there is a file system called NTFS, which can't be written by macOS but you can read it. So you encounter this case you can copy it but you can't copy files from Mac to the external hard drive.
Now let's try to check the file system: Finder > Right-click the drive and choose Get Info > Check the file system in the Format.
( 1 ) If it's listed as Windows NTFS file system.
You can use an NTFS driver for Mac like iBoysoft NTFS for Mac, which can directly and seamlessly read and write the drive on Mac without reformatting.
Or you can format it as other file systems like APFS, exFAT, or FAT32…But you will lose all the data, so do a backup before this step.
( 2 ) If it's not the NTFS-formatted drive, you can:
- Check the permissions.
- Free up more storage space for the external hard drive.
- Run First Aid to check and repair the drive.
- Update your Mac.
- Reformat the external drive.
Hope that you can copy files from the Mac to your drive.
Also read: Unable to Copy Files from Mac to External Hard Drive