That's a fair question and I wondered too. The way I understand it, it comes from multiple places :

> You agree not to [...] copy, adapt, modify, prepare derivative works based upon, distribute, license, sell, transfer, publicly display, publicly perform, transmit, stream, broadcast, attempt to discover any source code, reverse engineer, decompile, disassemble, or otherwise exploit the Service or any portion of the Service, except as expressly permitted in these Terms

Combined with

> All rights, title and interest in and to all materials that are part of the Service (including, but not limited to, designs, text, graphics, pictures, video, information, applications, software, music, sound and other files, and their selection and arrangement), except for Your Content, collectively referred to as the "Service Materials,” are, as between the Company and you, owned by the Company and/or its third party licensors.

And

> You agree that you shall not modify, copy, distribute, frame, reproduce, republish, download, scrape, display, post, transmit, or sell in any form or by any means, in whole or in part, or otherwise exploit the Service Materials without our express prior written permission. You acknowledge that you do not acquire any ownership rights by using the Service or by accessing any Service Materials posted on the Service [...]

Seem to ban client modifications, reverse engineering of the client, etc.

Then, the ToS make you agree to the Community Guidelines, in which you can find

> You may not use self-bots or user-bots to access Discord.

Which, from my understanding, is the main way third-party clients work. (Except for those simply embedding the discordapp website)

I might be wrong, but that's what I gathered from my small investigation