Why do anime have manga adaptations? Why don't authors just focus on one medium at a time? Instead of having to work on both the anime and the manga at the same time, why don't the authors just focus on one?
For this answer I am going to assume only works which began as an anime and were later adapted into manga are under consideration. This is hard to study nowadays because there are so few anime-original works, but in most of the cases I know of, the manga is just tie-in merchandise for the anime, the same way anime adaptations of manga are tie-in merchandise for the manga, or anime and manga adaptations of light novels and visual novels are tie-in merchandise for the light/visual novel. 

Usually, the author of the manga is a contract worker of some sort: the studio hires them to write and draw a manga version of the anime, sometimes while the production of the anime is underway, and sometimes after it's finished. The original team behind the anime doesn't usually work on the manga; their names might be on the cover as a "Story" credit, meaning they're just being acknowledged as the creator of the story. It's the reverse version of seeing "Based on the manga by XX" in the opening credits of an anime. So having a manga adaptation doesn't actually take any effort away from the anime; the two productions go ahead independently, sometimes extremely so. For example, the first manga adaptation of The Vision of Escaflowne was based on an early version of the story from when Yasuhiro Imagawa was attached as director. Imagawa left to direct G Gundam and the production was put on hold, but the manga went ahead with his shounen version of the story, only to become inaccurate later when Kazuki Akane came in and reworked the show as a shoujo series.

Some anime also have spinoff manga, which aren't directly based on the original anime. Evangelion, for example, has Angelic Days, Shinji Ikari Raising Project, and Campus Apocalypse. Madoka has Kazumi Magica, Oriko Magica, Wraith Arc, The Different Story, Homura Tamura, Homura's Revenge, Tart Magica, Suzune Magica, and probably soon the epic crossover Puella Magi Mahoro Magica: The Resurrection. Like the direct adaptation manga, these are passed off to hired help, but they often have valid creative reasons for existing. Angelic Days and Shinji Ikari Raising Project explored the banal world that Shinji creates in his mind in Episode 26 of the anime. Wraith Arc and The Different Story fill in parts of the anime storyline that weren't shown onscreen; Suzune Magica and Tart Magica focus on different characters in the same world; Homura Tamura is a parody. Since manga are cheaper to produce than anime, the spinoff manga are a low-cost way to explore the world of an anime, or create alternative scenarios, or to give hardcore fans something they want that doesn't have wide enough appeal to fund another anime. Some of these spinoff manga, I don't care about, but reading The Different Story totally changed my view of certain characters and events in the anime series, so I'm glad that the anime staff didn't decide to "just focus on one" and allowed the spinoff manga to be made.