Well I found it! In TVL, when Armand is telling Lestat and Gabrielle his story:

“In quiet allegiance to the Dark Ways, Armand
continued to serve. Yet in the centuries of his long obedience, Armand
kept two secrets to himself. These were his property, these secrets,
more purely his than the coffin in which he locked himself by day, or
the few amulets he wore. The first was that no matter how great his
loneliness, or how long the search for brothers and sisters in whom he
might find some comfort, he never worked the Dark Trick himself.
He wouldn’t give that to Satan, no Child of Darkness made by him.”

Hit the jump for more, cut for length.

Still in TVL, that quote above is right after he’s gone over how he’s seen so many vampires die:

In this particular, let
Armand observe that there was no vampire then living who was more
than three hundred years old. No one alive then could remember the
first Roman coven. The devil frequently calls his vampires home….

He had witnessed
the inevitable dissolution of covens, seen immortality defeat the most
perfectly made Children of Darkness, and it seemed at times some
awesome punishment that it never defeated him. Was he destined to
be one of the ancient ones? The Children of the Millennia? Could one
believe those stories which persisted still?

He’s also mentioned that the Dark Trick is not an exact science (also TVL):

But
let Armand understand here also that the effect of the Dark Trick is
unpredictable, even when passed on by the very young vampire and
with all due care. For reasons no one knows, some mortals when Born
to Darkness become as powerful as Titans, others may be no more
than corpses that move. That is why mortals must be chosen with
skill. Those with great passion and indomitable will should be avoided
as well as those who have none. 

So Armand’s reasons for refusing to turn Daniel, if you trust him to be honest about the ones he’s giving, seem to be that:

• Not everyone has the stamina for vampiring
• Mortal life is better and Daniel should appreciate it more!
• The Dark Trick is unpredictable and could leave Daniel in worse condition than mortal life ;A;
• Armand really underscores that mortal life is better, also bc of the tragedy he’s experienced in his own vampiring. 
• Armand has his own enemies to deal with (“I’m like any beast on the prowl. I have enemies who are older and
  stronger who would try to destroy me if it interested them to do so, I am sure.” – QOTD)
• There’s also the threat of extermination happening to alot of vampires in QOTD so... bad timing. (”What matters is that the end
  may be at hand…

  There is a vague repeated cry of
  danger, but no one seems to know whence it comes. They only know that we are being sought out and
  annihilated, that coven houses, meeting places, go up in flames.“ – QOTD)

Later, in QOTD, Daniel refers to it as a vow, maybe that’s he terminology Armand used when he told Daniel about it:

[Daniel says:] “Of course I believed you. The vow you made, you explained everything. But Armand, this is my question, to
whom did you make this vow?" 

Laughter. 

^He made the vow to himself ;A;

[Armand says:] "So you would have me break my vow. You would have what you think you want. But look well at this
garden, because once I do it, you’ll never read my thoughts or see my visions again. A veil of silence will
come down.”

1. I think this is definitively where Daniel realizes Armand’s not going to turn him:

Then the realization had come to Daniel as they stood together in the ruined dining room with its famous
murals of ritual flagellation barely visible in the dark: He isn’t going to kill me after all. He isn’t going to do it.
Of course he won’t make me what he is, but he isn’t going to kill me. The dance will not end like that.

2. Then Armand starts trying to get Daniel to understand his reasons for not wanting to give him the Dark Gift

“Give me what I want,” Daniel had demanded. 

“I’m giving you everything you could ever ask for." 

"Yes, but not what I have asked for, not what I want!" 

"Be alive, Daniel.” A low whisper, like a kiss. “Let me tell you from my heart that life is better than death.”

3. … which intensifies:

Ugly fights, terrible fights, finally, Armand broken down, glassy-eyed with silent rage, then crying softly but
uncontrollably as if some lost emotion had been rediscovered which threatened to tear him apart. “I will not
do it, I cannot do it. Ask me to kill you, it would be easier than that. You don’t know what you ask for, don’t
you see? It is always a damnable error! Don’t you realize that any one of us would give it up for one human
lifetime?