Root and intermediate certificates are both able to issue further certificates; the difference is that roots are installed directly in your OS/browser.
Though you shouldn't have a certificate called "Let's Encrypt" in your root certificate store, as it is called ISRG Root. (ISRG stands for Internet Security Research Group, and is the legal entity behind Let's Encrypt.)
This was a timely article but still left me confused.
And that's why your server needs to also send the intermediate certificate - so that clients can construct a chain of signatures from your website certificate to the root that is installed in the OS trust store.
This (the fact all end entity certificates are signed by an Intermediate, never a root) is a policy of the Web PKI rather than being inherent to any conceivable system for such a purpose or to the X.509 technology in particular.
Specifically the roots aren't allowed to be online by policy. So you can't use them to issue end entity certificates, when they do sign things (notably to create new Intermediates) that's a supervised activity, several humans (perhaps an officer from the organisation which owns the root, plus somebody representing their third party auditor, plus a technician to do the actual work) are typically physically present overseeing the signing process. The rest of the time the roots might live in a safe in somebody's office, that sort of thing.
This sort of safeguard means even catastrophic IT failures should only result in a compromised Intermediate. Still not good, but recoverable without needing to co-ordinate large numbers of third parties or greatly annoy the Relying Parties (ordinary people).