Apple Mail results in permanent fatal errors for some outgoing gmails

I use Apple Mail to send email, and my two gmail accounts sometimes bounce the email I send - but only to some of my friends' gmail accounts. The error message includes this wording:

 ----- The following addresses had permanent fatal errors -----

   (reason: 550-5.7.26 This mail is unauthenticated, which poses a security risk to the)

...

<<< 550-5.7.26 This mail is unauthenticated, which poses a security risk to the

<<< 550-5.7.26 sender and Gmail users, and has been blocked. The sender must

<<< 550-5.7.26 authenticate with at least one of SPF or DKIM. For this message,

<<< 550-5.7.26 DKIM checks did not pass and SPF check for [gmail.com] did not pass

<<< 550-5.7.26 with ip: [64.142.111.50]. The sender should visit

<<< 550-5.7.26 https://support.google.com/mail/answer/81126#authentication for

<<< 550 5.7.26 instructions on setting up authentication. o23-20020a637317000000b0054fd3dd12d4si755822pgc.799 - gsmtp

The instructions at the support.google webpage are incomprehensible to me.

Can anyone here help me?

I prefer using Apple Mail because I set it up to sort my incoming emails into many folders. I have not learned any way to similarly sort incoming email using gmail itself.

[Email Edited by Moderator]