Like Sollozzo, Roth simply couldn't allowed to live after attempting to have Michael killed. Like how Tom explained it to Kay at the end of the book, Sollozzo, Tessio, and Carlo alive would always be a threat against the "Family." so they had to go regardless of the cost.

By sending Rocco on a suicide mission to kill Roth, Michael, in effect, is killing two birds with one stone. First and foremost, he's rid of Roth and secondly, by taking the job to kill Roth, Rocco is redeeming himself for failing to protect Michael and his family during the botched assassination attempt at the Lake Tahoe compound. Also, Rocco was part of Clemenza's regime so his ties to Michael weren't as strong as Neri's were, making him, effectively, the odd man out.

As to why Michael didn't farm the hit out on Roth, it seems that it was simply too important to Michael to entrust to anyone who wasn't directly responsible to him.

I would also think that, like Pentangeli, Rocco would know his family would be taken care of if anything happened to him in the service of the Family. So that would be Michael's insurance against him turning informer. Although I seriously doubt either Rocco or Michael thought that he, Rocco, would be able to escape alive.