The main reason why we pray these two prayers in a low voice is that it is the tradition of the prophet (pbuh) and that he used to pray this way and has ordered us to pray exactly like him. Of course some reasons have been mentioned for this ruling in our hadiths, such as the fact that since the other three prayers are prayed when it is dark, it is necessary for them to be prayed aloud so that others can tell where the prayers are being held, while such a thing isn't necessary for prayers done during daytime. Yet none of these reasons that might factor into a certain ruling can't be considered the main reason for it, and in many cases, the main reasons for rulings remain unknown.
Many of the commands of Allah (swt) and/or His messengers are only for testing and examining the degree of His servants' servitude. For instance, in the story of Talut, he told his army that Allah (swt) was to test them with a stream of water; whosoever drank more than a handful of water was to be expelled from the army [and of course they were all very thirsty, so this was a big test for them]. In cases like this, one shouldn't seek a reason for such a command (of not drinking more than a handful of water) other than distinguishing the faithful from the weak and disobedient; such a reason seems convincing enough. Of course, this doesn't mean that this is the sole reason for all of Allah's (swt) commands and that everything He orders us to do is only to put us to the test. Many of Allah's (swt) commands are to the welfare and benefit of society and contribute to its development and perfection. Therefore, what was mentioned above was only to emphasize on the fact that merely not knowing the reasons behind some rulings doesn’t mean we can disregard them, although inquiring and researching about their reasons is commendable and is in no way in conflict with total submission to Allah (swt) and His commands.
Regarding the reason behind reciting fajr, maghrib and isha prayers aloud and dhuhr and asr prayers silently, there are different hadiths that we will list below:
Fazl ibn Shadhan reports Imam Ridha (as) speaking of the reason behind why some prayers are prayed silently; he said: "Prayers that are recited aloud are for when it is dark. It is necessary for these prayers to be recited aloud so that anyone who passes by can find out that congregational prayers are being held so he can join the rest if he likes. Therefore, if the darkness doesn’t let others find out about where prayers are being held, reciting them aloud will. Prayers that are held during the day don’t need to be recited aloud because everyone can easily locate where they are being held.
Of course, paying attention to this hadith might arouse some questions, namely: "Considering the circumstances of life today and that electricity doesn’t leave much of a difference between night and day, it no longer makes a difference to pray aloud or not.", or "This hadith's subject has to do with congregational prayers and has nothing to do with furada (solitary) prayers." , or "One can find benefits in reciting prayers held during the day aloud, such as helping the blind find where the prayers are being held etc.".
The answer to these questions is that the ruling of reciting day and night prayers aloud or silently cannot be altered just because of some of the questions that might surround it, because first of all, there is nothing that can verify that the reason mentioned in the hadith by Imam Ridha (as), is the sole reason for such a ruling (if it was, one could say that now since there are no lighting problems as in the past, then it is no longer needed to pray night prayers aloud). There are chances that there are other reasons for this ruling that we don’t know about [just because a reason has been mentioned, doesn’t disprove that there are other reasons]. Secondly, there are still places today that don’t have electricity like we do, thus reciting aloud still holds such benefits. As a result, this ruling falls in the category of those rulings that need to be abided by just because Allah (swt) has asked us to do so, in order to prove our loyalty to Him and the tradition of His prophet (pbuh).
There are also other hadiths that mention other reasons for this ruling, such as: "During the Mi'raj [the prophet's (pbuh) ascension], the angels followed the prophet (pbuh) in some of his prayers, and in order to show the significance of these prayers and their higher rank compared to others, Allah (swt) ordered them to be recited aloud.
In closing, we would like to stress on this point one more time that the major reason for Allah's (swt) rulings, is the total submission to His will without any questions asked, or else a great majority of Islamic rulings can be questioned similarly. For instance, why is it mandatory to recite surah Fatihah in every prayer's opening, while it is permissible to choose any surah to recite after it? Why is it that in the prayer, one cannot turn his/her head away from the qiblah? Why do those praying behind the imam of congregational prayers have to be silent while the surahs are being recited, but have to recite the rest of the prayer themselves?...and so on.
The main reason for such rulings, is that they are the tradition of the prophet (pbuh) (unless the reason has been clearly stated in the Quran); since his actions and worships were so, we do the same. He has been introduced as our guide and role model by Allah (swt) and we have been ordered to follow him, and he himself has said: "Pray the way you see me pray.", therefore we have to pray and act the way he used to.
 Muhammad ibnil-Hasan Hurr Al-Ameli, Wasa'ilul-Shia, vol.6, pp.82-83, hadith 7406.
 As the Usuli scholars put it, it isn't Mansusul-Illah.
 Muhammad ibnil-Hasan Hurr Al-Ameli, Wasa'ilul-Shia, vol.6, pp.82-83, hadith 7407.
 Allamah Majlisi, Biharul-Anwar, vol.82, pg.279; Ibn Abil-Jumhur Ahsa'i, Awalilla'ali, vol.3, pg.85.