Mainly because scientists have focused on reading and invented clever technologies to do so. The guy who made the reading breakthrough, Craig Venter, is also a writing pioneer in his synthetic biology work.
Earlier this year there was a secret meeting ran by a Harvard prof to launch the DNA-WRITE project to improve write technology. The meeting was secret because it was feared that anti-GMO groups and general Frankenstein fear might quash the efforts prematurely.
P.S. Some computer write memory technologies are also much slower than reading.