For the hundredth time - or so it seemed to [Moiraine] - she considered the words to use. "Before we left Tar Valon I made arrangements, should anything happen to me, for your bond to pass to another." [Lan] stared at her, silent. "When you feel my death, you will find yourself compelled to seek her out immediately. I do not want you to be surprised by it."
"Compelled," he breathed softly, angrily. "Never once have you used my bond to compel me. I thought you more than disapproved of that."
"Had I left this thing undone, you would be free of the bond at my death, and not even my strongest command to you would hold. I will not allow you to die in a useless attempt to avenge me. And I will not allow you to return to your equally useless private war in the Blight. The war we fight is the same war, if you could only see it so, and I will see that you fight it to some purpose. Neither vengeance nor an unburied death in the Blight will do.
Moiraine and Lan, The Great Hunt, p. 271
One of the more challenging (and sometimes least enjoyable) parts of leadership is having conversations like this with individual team members. I would argue that a conversation along this sort of path is even more challenging. The conversations about discipline or job performance aren't fun, but they are usually fairly straightforward. Conversations about future events or possibilities tend to elicit more emotion as they are more nebulous, not necessarily originating in any documented procedure or guideline. In this instance, Moiraine is planning far in advance to ensure that Lan's skills don't go to waste. And it drives the reserved man to fury:
"Is that what this has been for?" he grated. His eyes burned like blue fire, and his mouth twisted. Anger; for the first time ever that she had seen, open anger etched his face. "Has all this talk been a test - a test! - to see if you could make my bond rub? After all this time? From the day I pledge to you, I have ridden where you said ride, even when I thought it foolish, even when I had reason to ride another way. Never did you need my bond to force me. On your word I have watched you walk into danger and kept my hands at my sides when I wanted nothing more than to out sword and carve a path to safety for you. After this, you test me?"
Lan, The Great Hunt, p. 272-273
The relationship between Moiraine and Lan is founded on mutual respect; as a man of his word, Lan doesn't need compulsion to do anything. I think it's even less about the fact that Moiraine intends to compel him through the bond, it's that she considers it a requirement - as if his word means nothing! - drives Lan's anger. Moiraine definitely could have handled this better; other than to actually test him, there was no real reason to get Lan angry. It's clear that he didn't understand the deeper nature of the Warder's bond; but that information could have been presented in a much cleaner fashion than simply throwing it all in his face. Part of that was likely Moiraine's very natural reaction to simply cut right to the chase; however being overly blunt in the eagerness to "get through" the conversation reduces the overall effectiveness of the conversation. The conversation that needs to happen is exactly in that uncomfortable area for everyone. It's just not always pleasant.