why is yahoo answers shuting down?

Because Verizon Media is choosing to shut it down (just as they did Yahoo Messenger and Yahoo Groups). No specific explanation was given, but considering the significant decline in quality of content on the site versus the cost of cleaning it up and keeping it running, it's not a surprise (a disappointment, but not a surprise). 

Yahoo Answers has not been doing well Lately a lot of Users have Left Poor Maintenance of the

Site they have not Fixed a lot of the Problems they are Likely Losing Money on it as well so

They feel its Best to Close it Down If there not going to Fix it they minus as well Close it

Down

New laws are coming out that will hold social media sites responsible ( libel) to clean up what is posted ( racism. slander, abuse ,porn etc...FAST or face fines = $$$$$$$$$$$

The major reason has to do with money/cost.  Yahoo has been taking about it for years.