I've read that they don't want to send it to the USA because of the possibility of Boeing to unduly influence the investigation.

http://fortune.com/2019/03/13/ethiopian-air-crash-black-boxe... > but Ethiopian authorities would prefer to work with the U.K.’s Air Accidents Investigation Branch to ensure that U.S. experts won’t have undue influence in the probe of the American-made plane.

https://www.bloomberg.com/news/articles/2019-03-13/ethiopia-... > The choice of Europe over the U.S. National Transportation Safety Board for the analysis of the black boxes is a strategic decision for Ethiopian Airlines and the nation’s government, said Asrat Begashaw, the carrier’s public relations director.