How would you break it to someone that their DPS is awful?

[Souljacker]

I approach it like asking for help with the class myself.

"Hey X, I'm working on my [job] rotation. You like playing [job]. What do you do? Do you use this [link] or something else?"

That just gives the player completely the opposite impression from what the OP is trying to do. The player isn't successful at DPS, and frankly, it sounds like he might not be very successful at life, either if he can't take constructive criticism. I'm always for spelling out the truth in a tactful way. Express to him how valuable he is to the group, but be clear that his DPS skills are not up to the level his tanking skills are. If he really is so delicate that you can't improve him without him falling apart - he (and you) are going to have bigger problems down the line both in RL and in the guild.

[Sagittarian]

That just gives the player completely the opposite impression from what the OP is trying to do.

It's just the opener so they don't start on the defensive. It would then be followed up with pointed questions like "Just flare not swiftcast+flare?", "Isn't flare less efficient for single targets?", or "Blizzard 1? Why not blizzard 3 to get a full stack of ice?". I've found it more effective with certain personality types.
And I'm assuming this a /tell conversation. If in group chat then I'd ask everyone with that job to chime in with what they think is best.

I've seen so many people use flare against a single target without even using swiftcast.... I sit there and watch their cast bar for 4 seconds in utter amazement.