Once upon a time, an academy graduate whose father was from another service could receive a commission in that service, sort of professional courtesy. It was rare and perhaps even more rare these days. A few others transfer to another service after some passage of time.
Billy Mitchell (real name), USMA Class of ?? served with the 1st Infantry Division in Vietnam as an Infantry Platoon Leader. He served a second tour as a Captain, advisor to a Vietnamese Ranger Battalion. After that tour, he was assigned to the Florida Ranger Camp at Eglin AFB. He tried to get into Army flight school, but they had plenty of teenaged Warrant Officers, so no deal. Some Air Force friends told him that the USAF was desperate for pilots and he asked for a transfer and flight school. The USAF said yes, and he served a third tour driving an F4. I met him in Europe when he was flying F15’s.
Would be an interesting story to find out why he did what he did: USAFA then SF, or SF as an enlisted then USAFA commission. . .and then what? Wiki has a confusing writeup about him and as far as I can find, no mention of USAFA, and while mentioning “former SF” there is no detail other than as a journalist doing field work with them.
His linkedin profile doesn't add much; https://www.linkedin.com/profile/view?id=37913327&authType=NAME_SEARCH&authToken=S7E9&locale=en_US&trk=tyah&trkInfo=clickedVertical%3Amynetwork%2Cidx%3A1-1-1%2CtarId%3A1436375579773%2Ctas%3AChuck%20de%20Caro
Would be interesting to read about his active-duty time.
One of the more common reasons today is marriage. For example, an Air Force graduate marrying an Army graduate or officer can get an Army commission, because it's easier to station them together.