How is it that Email Marketing Platforms like mailchimp are able send emails from me without me giving them my email password?

Solution 1:

Most of these services need you to authenticate your email domain. The process includes updating DNS records to add information that allows their servers to send mail from your address without being marked as spam.

Depending on the service they may add their server information to your SPF record, create a DMARC key, and/or add CNAME records that point to them.

Since you mentioned Mailchimp, here is a link to their help page explaining the process. https://mailchimp.com/help/set-up-custom-domain-authentication-dkim-and-spf/

Without doing these types of things the best they should be able to do is send-on-behalf. Which will still show your name but may also add a "on behalf of" or "via" added.