This lack of authentication is what allows for all the spam with forged From: headers. You can, for example, send an e-mail from the command-line using telnet[1] and have it appear to be from any e-mail address you wish.
In the last several years there have been several attempts to address this such as DomainKeys[2], DKIM[3], SPF[4], and DMARC[5].
As for why Google allows the message through, well, you'd have to ask them.
[0]: https://www.ietf.org/rfc/rfc733.txt
[1]: https://workaround.org/ispmail/lenny/test-mail-through-telne...
[2]: https://en.wikipedia.org/wiki/DomainKeys
[3]: https://en.wikipedia.org/wiki/DomainKeys_Identified_Mail