**MAJOR SPOILER WARNING**
There are 2 situations where you can get this. The first is on Virmire. Wrex is angry that the cure for the genophage will be destroyed. If you've completed the Wrex's Armor sidequest, choose the left-side options that appear. If not, have at least 8 in charm or intimidate, and use those.
Later when the citadel is sieged, you will talk with Saren. You will have to use about 3 successive persuades to get him to kill himself. High persuasion skill is needed. If you charmed/intimidated him on Virmire these persuasions will be easier.
Edit: If you've completed the Family Armor assignment, the right side options work as well. (Thanks to Mental Knight 5)
If you choose the lower-left option, 'This isn't up for debate,' Wrex does not stand down, and you must persuade him to save him.