1. decentralising the conversation so no single entity owns or controls it: being a federated communication database rather than a messaging platform. 2. making bridging a first class citizen (hence the name Matrix; it's designed to matrix together other conversations) 3. providing a deliberately monolithic spec to try to avoid fragmentation and help us evolve it relatively rapidly.
Now, I have huge respect for you in showing that it's possible to build a good UX on top of XMPP. And we don't think XMPP is fundamentally flawed. But we wanted to try a completely different architecture and design and see if it flies. As per the earlier comment I see it very similar to NNTP and SMTP. They can be both used to power conversations, but architecturally they couldn't be more different, and the world is big enough for both.
Genuine question: any idea how big the public XMPP federation is in terms of active servers and active users? Would be interested to know how Matrix compares.