Why the Muslim woman must pray every time with a low voice, while the Muslim man can pray in aloud voice during some prayers like Aa'ishah for example.

All perfect praise be to Allaah, The Lord of the Worlds.  I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

A woman is not obliged to perform the prayer silently in all cases, there are some details given by the scholars on this issue.  For instance if the woman is alone, or in the presence of her Mahaarim (non-marriageable relatives), or that she leads other women in prayer, then reciting aloud in the prayers where one should recite loudly is recommended in her regard, exactly like man.  However, if the woman is in the presence of marriageable men, then some scholars disliked her to recite loudly in the prayer in order to avoid causing temptation.  Some other scholars forbade her to recite loudly if she fears to cause temptation by reciting aloud.  The evidence of the scholars who forbade her or disliked her to recite loudly in the presence of marriageable men is the Prophetic narration in which the Prophet said: "Men should say Subhaanallaah (Praise be to Allaah) while women should clap their hands (This is during the congregational prayer)."  [Al-Bukhari and Muslim]  They argued that since is it not permissible for her to say Subhaanallaah in order to attract the attention of the Imaam if he made a mistake in the prayer, taking into account that it is an obligation to correct him, then it is more appropriate that it is not permissible for her to recite loudly when performing the prayer as this is not an obligation.  The scholars also gave the evidence of the agreement of the scholars that she is not allowed to call the Athaan (call to the prayer) nor say the Talbiyyah (saying: "Here I am O Allaah, (in response to Your call), here I am.  Here I am, You have no partner, here I am.  Verily all praise, grace and sovereignty belong to You.  You have no partner").  Loudly (when she performs Hajj), and in other places where (marriageable) men are present.

Allaah Knows best.