The reason why Qur’aan is recited out loud in the nighttime prayers and silently in the daytime prayers

Firstly: 

The Muslim is required
to follow the Prophet (peace and blessings of Allaah be upon him) and
follow his example, whether he knows the reason behind a ruling or he does
not. Allaah says (interpretation of the meaning): 

“Indeed in the Messenger
of Allaah (Muhammad) you have a good example to follow for him who hopes for
(the Meeting with) Allaah and the Last Day, and remembers Allaah much”

[al-Ahzaab 33:21] 

He should also be certain that Islam is based on great
wisdom, but this wisdom may be known to us or we may be unaware of it, or we
may know some of it and not the rest of it. 

There is nothing wrong with a person asking the reason and
trying to find out, because knowing it will increase his knowledge and peace
of mind. 

Secondly: 

Some of the scholars have pondered the reason why Qur’aan is
recited out loud in the nighttime prayers and silently in the daytime
prayers, and the summary of what they have mentioned concerning that is: 

The night is a time when people are quiet, alone and more
focused, so it is prescribed to recite Qur’aan out loud at that time so as
to make manifest the pleasure of a person’s conversing with his Lord, and so
that the heart, tongue and ears will be involved in the recitation. 

This meaning is suggested by the verse in which Allaah says
(interpretation of the meaning): 

“Verily, the rising by night (for Tahajjud prayer) is very
hard and most potent and good for governing oneself, and most suitable for
(understanding) the Word (of Allaah).

7. Verily, there is for you by day prolonged occupation
with ordinary duties”

[al-Muzzammil 74:6-7] 

Ibn Katheer said: 

The point is that this rising may be at any time of night.
What is meant here is that when praying at night, both the heart and the
tongue are focused on the recitation, hence Allaah says (interpretation of
the meaning): “is very hard and most potent and good for governing
oneself, and most suitable for (understanding) the Word (of Allaah)”
i.e., the mind will be more focused when reciting and will understand the
words more than during the day, which is a time when people move about and
there is a great deal of noise, and it is the time of seeking provision. End
quote. 

Al-Qurtubi (19/40) said: 

What is meant is that the heart, sight, hearing and tongue
work together in harmony when reciting Qur’aan, because voices and movements
are stilled. End quote. 

Al-Sa’di (may Allaah have mercy on him) said (p. 1058): “Verily,
the rising by night (for Tahajjud prayer) is very hard and most potent and
good for governing oneself, and most suitable for (understanding) the Word
(of Allaah)” i.e., it is more likely to achieve the purpose of the
Qur’aan, where both heart and tongue are focused, because there are fewer
distractions, one can understand what one recites, and does the prayer
properly. 

This is unlike the day, when these purposes cannot be
achieved. Hence Allaah says “Verily, there is for you by day prolonged
occupation with ordinary duties” – i.e., going about to attend to your
needs and living, which means that the heart is distracted and cannot focus
fully. End quote.  

It says in Tuhfat al-Muhtaaj: 

There remains the wisdom
behind reciting out loud – what is it? It may be that it is because night is
the time when one is alone and people get together for lighthearted talk. So
it is prescribed to recite Qur’aan out loud at that time so as to make
manifest the pleasure of a person’s conversing with his Lord. This applies
only to the first two rak’ahs because the worshipper has more energy then.
Because the day is the time of distractions and mixing with people, it is
required to recite silently, because the daytime is not the best time to
focus fully on conversing with Allaah. The morning (Fajr) prayer is joined
to the night prayers because its time is not usually a time when there are
distractions, like Friday. End quote. 

Ibn al-Qayyim (may Allaah have mercy on him) said in
I’laam al-Muwaqqi’een (2/91): 

With regard to the distinction between the nighttime prayers
and the daytime prayers, in terms of reciting out loud and reciting
silently, there is great wisdom in that, because the night is a time when
voices and movements are stilled, and hearts are focused and have renewed
energy. The day is the time when people are busy with their day-to-day
occupations, and the night is the time when a person can focus with his
heart on what he is saying with his tongue. Hence the Sunnah is to make the
recitations in Fajr longer than in other prayers. The Messenger of Allaah
(peace and blessings of Allaah be upon him) used to recite between
sixty and one hundred verses in them, and Abu Bakr used to recite al-Baqarah
in them, and ‘Umar used to recite al-Nahl, Hood, Bani Israa’eel, Yoonus and
similar soorahs, because the heart is more free of distractions when it has
just been wakened from sleep. If the first thing that a person hears is the
word of Allaah in which there is all goodness, then these words will come to
his heart which is free form any distraction, and will thus have a great
impact on him. As for the day, the opposite is the case, so Qur’aan is
recited silently unless there is a reason, such as the large gatherings on
Eid and Jumu’ah (Friday), and when offering prayers for rain and the eclipse
prayer. On those occasions it is better to recite out loud and that is more
likely to achieve the objective and is more beneficial, and because this
serves to convey the words of Allaah when there is a large gathering. End
quote. 

May Allaah increase us and you in beneficial knowledge and
righteous deeds. 

And Allaah knows best.