user-1: In MN 138, the Buddha said this:

The Blessed One said: "Monks, I will teach you a statement & its analysis. Listen & pay close attention. I will speak."
"As you say, lord," the monks responded.
The Blessed One said this: "A monk should investigate in such a way that, his consciousness neither externally scattered & diffused, nor internally positioned, he would from lack of clinging/sustenance be unagitated. When — his consciousness neither externally scattered & diffused, nor internally positioned — from lack of clinging/sustenance he would be unagitated, there is no seed for the conditions of future birth, aging, death, or stress."
That is what the Blessed One said. Having said it, the One Well-gone got up from his seat and went into his dwelling.
Then, not long after the Blessed One had left, this thought occurred to the monks: "This brief statement the Blessed One has made, after which he went into his dwelling without analyzing the detailed meaning

I thought the Buddha always kept his promises. Why didn’t he analyze the statement when he said he would?

user471: From the MN 58 quote below, we see that the Buddha has a sense of proper time for saying things which are factual, true and beneficial.
So, we can only surmise that the Buddha gave a statement without its detailed analysis, to give the monks time to think about his statement, before explaining to them the detailed analysis at a proper time, later. Why is that? It's because he has compassion for the monks.

In the case of words that the Tathagata knows to be factual, true,
beneficial, but unendearing & disagreeable to others, he has a sense
of the proper time for saying them.
In the case of words that the Tathagata knows to be factual, true,
beneficial, and endearing & agreeable to others, he has a sense of the
proper time for saying them. Why is that? Because the Tathagata has
sympathy for living beings."


user13709: He did analyze it. His exposition was to return to his hut and simply move on without being externally or internally bound. This is very similar to the Zen story about kicking over the water jug.

When Master Guishan was under Baizhang, he had the position of tenzo [cook]. Baizhang wanted to choose a master for Great Gui Mountain in the province of Konan. He called the head monk and the rest of his disciples together to have them present their views and said that the outstanding person should be sent.
Then he took a water jug, put it on the floor, and said, “You may not call this a water jug. What will you call it?”
The head monk said, “It cannot be called a wooden sandal.”
Baizhang then asked Guishan. Guishan immediately kicked over the water jug and left.
Baizhang laughed and said, “First monk, you have been defeated by Guishan.”
So he ordered Guishan to found the new monastery.

The Buddha's analysis was straightforward and direct. Effectively he told us to understand this teaching ourselves through direct insight and ongoing practice, without further ado, and certainly without extra babble.

user19480: First, a disclaimer: I cannot give assurance that this answer is found in Theravada Buddhism, as your question is tagged, nor am I answering the question in the title. I am answering the question you pose at the end of your description: “Why didn’t he analyze the statement when he said he would?”
The Buddha said: “I will teach you a statement & its analysis.” He did not say that those were two different things. In fact, the statement is the analysis of itself. It tells us how to investigate. Investigate what? Investigate the Dharma, that which the Buddha was teaching. He gives directions on how to do it, by training our mind so that it is not externally, nor internally fixed, and therefore without attachment to views or understandings (sustenance) that feed our discursive thoughts.  For example, by being attached to the understanding that analyzing a statement is something done in a procedural way, rather than by an intuitive insight about its meaning.
Here is a quote from the Mahayana, found in the Surangama Sutra:

Ananda, if you are now desirous of more perfectly understanding Supreme Enlightenment and the enlightening nature of pure Mind-Essence, you must learn to answer questions spontaneously with no recourse to discriminating thinking. For the Tathagatas in the ten quarters of the universes have been delivered from the ever returning cycle of deaths and rebirths by this same single way, namely, by reliance upon their intuitive minds.”


user254: Those are two sentences. Perhaps the first is the statement and the second the analysis.

Also in the Pali it's a single compound word:

Mendicants, I shall teach you the analysis of a recitation passage.
uddesavibhaṅgaṁ vo, bhikkhave, desessāmi.


uddesa

recitation, instruction; indication; brief indication, brief statement;
summary exposition instructing, specifying; inviting; food for a specific person



vibhaṅga
distribution; division; classification

So maybe there's no promise of a separate analysis -- it's just the word they use, like "explanation" or "dhamma-talk" or something like that, and this one happened to be a very short one.
Also I wonder whether uddesa is necessarily always verbal (apparently they often are, so often that one was expected) -- whether this might be a teaching-by-example instead of a verbal analysis.

-1: <p>In <a href="https://www.accesstoinsight.org/ati/tipitaka/mn/mn.138.than.html" rel="nofollow noreferrer">MN 138</a>, the Buddha said this:</p>
<blockquote>
<p>The Blessed One said: &quot;Monks, I will teach you a statement &amp; its <strong>analysis</strong>. Listen &amp; pay close attention. I will speak.&quot;</p>
<p>&quot;As you say, lord,&quot; the monks responded.</p>
<p>The Blessed One said this: &quot;A monk should investigate in such a way that, his consciousness neither externally scattered &amp; diffused, nor internally positioned, he would from lack of clinging/sustenance be unagitated. When — his consciousness neither externally scattered &amp; diffused, nor internally positioned — from lack of clinging/sustenance he would be unagitated, there is no seed for the conditions of future birth, aging, death, or stress.&quot;</p>
<p>That is what the Blessed One said. Having said it, the One Well-gone got up from his seat and went into his dwelling.</p>
<p>Then, not long after the Blessed One had left, this thought occurred to the monks: &quot;This brief statement the Blessed One has made, after which he went into his dwelling without <strong>analyzing</strong> the detailed meaning</p>
</blockquote>
<p>I thought the Buddha always kept his promises. Why didn’t he analyze the statement when he said he would?</p>
 471: <p>From the <a href="https://www.accesstoinsight.org/tipitaka/mn/mn.058.than.html" rel="nofollow noreferrer">MN 58</a> quote below, we see that the Buddha has a sense of proper time for saying things which are factual, true and beneficial.</p>
<p>So, we can only surmise that the Buddha gave a statement without its detailed analysis, to give the monks time to think about his statement, before explaining to them the detailed analysis at a proper time, later. Why is that? It's because he has compassion for the monks.</p>
<blockquote>
<p>In the case of words that the Tathagata knows to be factual, true,
beneficial, but unendearing &amp; disagreeable to others, he has a sense
of the proper time for saying them.</p>
<p>In the case of words that the Tathagata knows to be factual, true,
beneficial, and endearing &amp; agreeable to others, he has a sense of the
proper time for saying them. Why is that? Because the Tathagata has
sympathy for living beings.&quot;</p>
</blockquote>
 13709: <p>He did analyze it. His exposition was to return to his hut and simply move on without being externally or internally bound. This is very similar to the Zen story about <a href="https://www.bowzwestchester.org/2016/03/mar-29-apr-4-gg-40.html" rel="nofollow noreferrer">kicking over the water jug.</a></p>
<blockquote>
<p>When Master Guishan was under Baizhang, he had the position of tenzo [cook]. Baizhang wanted to choose a master for Great Gui Mountain in the province of Konan. He called the head monk and the rest of his disciples together to have them present their views and said that the outstanding person should be sent.
Then he took a water jug, put it on the floor, and said, “You may not call this a water jug. What will you call it?”<br />
The head monk said, “It cannot be called a wooden sandal.”<br />
Baizhang then asked Guishan. Guishan immediately kicked over the water jug and left.<br />
Baizhang laughed and said, “First monk, you have been defeated by Guishan.”
So he ordered Guishan to found the new monastery.</p>
</blockquote>
<p>The Buddha's analysis was straightforward and direct. Effectively he told us to understand this teaching ourselves through direct insight and ongoing practice, without further ado, and certainly without extra babble.</p>
 19480: <p>First, a disclaimer: I cannot give assurance that this answer is found in Theravada Buddhism, as your question is tagged, nor am I answering the question in the title. I am answering the question you pose at the end of your description: “Why didn’t he analyze the statement when he said he would?”</p>
<p>The Buddha said: “I will teach you a statement &amp; its analysis.” He did not say that those were two different things. In fact, the statement is the analysis of itself. It tells us how to <em>investigate</em>. Investigate what? Investigate the Dharma, that which the Buddha was teaching. He gives directions on how to do it, by training our mind so that it is not externally, nor internally fixed, and therefore without attachment to views or understandings (sustenance) that feed our discursive thoughts.  For example, by being attached to the understanding that analyzing a statement is something done in a procedural way, rather than by an intuitive insight about its meaning.</p>
<p>Here is a quote from the Mahayana, found in the Surangama Sutra:</p>
<blockquote>
<p>Ananda, if you are now desirous of more perfectly understanding Supreme Enlightenment and the enlightening nature of pure Mind-Essence, you must learn to answer questions spontaneously with no recourse to discriminating thinking. For the Tathagatas in the ten quarters of the universes have been delivered from the ever returning cycle of deaths and rebirths by this same single way, namely, by reliance upon their intuitive minds.”</p>
</blockquote>
 254: <p>Those are two sentences. Perhaps the first is the statement and the second the analysis.</p>
<hr />
<p>Also in the Pali it's a single compound word:</p>
<blockquote>
<p>Mendicants, I shall teach you the analysis of a recitation passage.</p>
<p>uddesavibhaṅgaṁ vo, bhikkhave, desessāmi.</p>
</blockquote>
<blockquote>
<p><a href="https://suttacentral.net/define/uddesa" rel="nofollow noreferrer">uddesa</a></p>
<ol>
<li>recitation, instruction; indication; brief indication, brief statement;</li>
<li>summary exposition instructing, specifying; inviting; food for a specific person</li>
</ol>
</blockquote>
<blockquote>
<p><a href="https://suttacentral.net/define/vibha%E1%B9%85ga" rel="nofollow noreferrer">vibhaṅga</a><br />
distribution; division; classification</p>
</blockquote>
<p>So maybe there's no promise of a separate analysis -- it's just the word they use, like &quot;explanation&quot; or &quot;dhamma-talk&quot; or something like that, and this one happened to be a very short one.</p>
<p>Also I wonder whether <em>uddesa</em> is necessarily always verbal (apparently they often are, so often that one was expected) -- whether this might be a teaching-by-example instead of a verbal analysis.</p>
