Tirmidhi

1:
Here, one objection is that Eid occurs in Shawwal, so how has Ramadan been called the "month of Eid"? The answer to this is that it is due to proximity; since Eid is realized only because of Ramadan, it has thus been attributed to it.

2:
An objection to this is that sometimes both months are twenty-nine (29) days, so the answer given is that what is meant is that generally both are not short.

3:
And this does indeed happen.

Hadith Commentary:
What is meant are the two months of Ramadan and Dhu al-Hijjah.

Hadith Commentary:
(1)
Imam Bukhari rahimahullah has narrated this hadith through two chains: one from Ishaq bin Suwayd and the other from Khalid Hadhdha’. However, he has only mentioned the text from the narration of Khalid Hadhdha’. The narration of Ishaq bin Suwayd has been mentioned by Abu Nu‘aym in his Mustakhraj, which states that the months of Ramadan and Dhu al-Hijjah are not less (than their full days). Since the wording of this narration differs, Imam Bukhari rahimahullah chose the narration of Khalid Hadhdha’ for the text because there is no difference in its wording. Although the month of Shawwal is the month of Eid, it is attributed to the month of Ramadan.

(2)
The meaning of this hadith is that although the number of days may be less, in terms of the perfection of worship, the ruling for both is the same. If someone fasted for twenty-nine days, he will receive the reward of thirty fasts. No one should have any doubt regarding its reward; similarly, if there is a mistake in the standing at ‘Arafah (wuquf ‘Arafah), his Hajj is complete and there is no deficiency in it. (Fath al-Bari: 4/161)

Hadith Commentary: Benefits and Issues: According to some, the meaning of this hadith is that Ramadan and Dhu al-Hijjah are always thirty, thirty days each. However, this interpretation is completely contrary to reality and observation. Therefore, this meaning cannot be intended. According to Imam Ahmad rahimahullah, the meaning is that both are not short at the same time; if one is twenty-nine days, then the other will necessarily be thirty (30) days. But this too is contrary to observation and reality, as both months can be twenty-nine days in the same year. The correct view is that of Imam Ishaq ibn Rahwayh rahimahullah: whether the month is twenty-nine or thirty days, the reward and merit are not diminished. Or, it may mean that their rulings are the same in both cases. Or, the intent may be that, generally, both are not twenty-nine days each. Occasionally, this can happen as well. And consideration is given to what is general and most common.

Benefits and Issues:
There are several opinions regarding the explanation of this hadith.
The summary of the insights of Hafiz Ibn Qayyim rahimahullah is as follows.

➊ These two months are not both twenty-nine days in the same year.
This is also the opinion of Imam Ahmad.

➋ This statement is in the sense of predominance, meaning that generally they are not both deficient (i.e., twenty-nine days) together.
If it ever does happen, it is rare.

➌ A group of scholars holds the view that the statement of the Prophet sallallahu alayhi wa sallam was specific to that particular year.

➍ These two months are not deficient in reward and merit, even if they are only twenty-nine days in count.
With Allah, the reward is complete.

➎ By this statement is meant the virtue of the first ten days of Dhu al-Hijjah, that the reward for deeds in these days is equal to that of Ramadan.
However, comparatively, it is said that between the last ten nights of Ramadan and the first ten days of Dhu al-Hijjah, the nights of Ramadan are superior, because they contain Laylat al-Qadr.
And the Prophet sallallahu alayhi wa sallam would devote himself to worship in these nights in a manner unlike any other time.
And in terms of days, the first ten days of Dhu al-Hijjah are superior, because in the hadith the day of sacrifice (Yawm al-Nahr) is called the greatest of days.
And the virtue of the Day of Arafah is also well-known and established.

➏ Since these months and days are among the most beloved days to Allah, and the deeds performed in them are greatly blessed,
therefore, as encouragement, it has been stated that one should not be concerned about their being more or less in number, but rather strive to excel in good deeds.
There is no deficiency in reward and merit in these two months.

Benefit:
The explanation of this Prophetic statement (sallallahu alayhi wa sallam) has been given in various ways.

According to one opinion, the meaning of the hadith is that even if the months are of twenty-nine days, they are still great in terms of honor and reward. Do not consider them insignificant.

A second meaning that has been stated is that in one year, both months are not of twenty-nine days. If one of these months is of twenty-nine days, then the other will certainly be of thirty days. This meaning is also correct to some extent, because generally this is what happens.

The first meaning appears to be more correct, because in Ramadan the worship of fasting is performed, and in Dhu al-Hijjah the worship of Hajj is performed, and both of these are among the pillars of Islam, whereas the other pillars of Islam are not related to any specific month.