Why didn't Maxis make The Sims 3?

The Sims 3, along with The Sims 3 World Adventures, was made by Electronic Arts, primarily EA Blackbox (EA Canada) and Visceral Games (owned by Electronic Arts).

Maxis had nothing to do with the Sims 3, unfortunately. Maxis made The Sims (including all expansions) and The Sims 2 (including all expansions)

EA only published The Sims and Sims 2 (all expansions), they never created anything about it.