Getting an education is considered a fundamental right of every man and woman and it is a virtue to get educated. But if we talk about coeducation in the context of below hadith and ayah of the Holy Qur'an it may cause harm.
The importance of haya (modesty) can be found in this Sahih hadith:
Sahih Al-Bukhari Volume 8::Book 73::Hadith 138:
عَنْ قَتَادَةَ، عَنْ أَبِي السَّوَّارِ الْعَدَوِيِّ، قَالَ سَمِعْتُ عِمْرَانَ بْنَ حُصَيْنٍ، قَالَ قَالَ النَّبِيُّ صلى الله عليه وسلم " الْحَيَاءُ لاَ يَأْتِي إِلاَّ بِخَيْرٍ ". فَقَالَ بُشَيْرُ بْنُ كَعْبٍ مَكْتُوبٌ فِي الْحِكْمَةِ إِنَّ مِنَ الْحَيَاءِ وَقَارًا، وَإِنَّ مِنَ الْحَيَاءِ سَكِينَةً. فَقَالَ لَهُ عِمْرَانُ أُحَدِّثُكَ عَنْ رَسُولِ اللَّهِ صلى الله عليه وسلم وَتُحَدِّثُنِي عَنْ صَحِيفَتِكَ.
Narrated Abu As-Sawar Al-Adawi: 'Imran bin Husain said, "The Prophet said, 'Haya' does not bring anything except good." Thereupon Bashir bin Ka'b said, 'It is written in the wisdom paper: Haya leads to solemnity; Haya leads to tranquility (peace of mind)." 'Imran said to him, "I am narrating to you the saying of Allah's Apostle and you are speaking about your paper (wisdom book)?"
and in the Qur'an too:
قُل لِّلْمُؤْمِنِينَ يَغُضُّوا مِنْ أَبْصَارِهِمْ وَيَحْفَظُوا فُرُوجَهُمْ ۚ ذَٰلِكَ أَزْكَىٰ لَهُمْ ۗ إِنَّ اللَّـهَ خَبِيرٌ بِمَا يَصْنَعُونَ ﴿٣٠﴾ وَقُل لِّلْمُؤْمِنَاتِ يَغْضُضْنَ مِنْ أَبْصَارِهِنَّ وَيَحْفَظْنَ فُرُوجَهُنَّ وَلَا يُبْدِينَ زِينَتَهُنَّ إِلَّا مَا ظَهَرَ مِنْهَا ۖ وَلْيَضْرِبْنَ بِخُمُرِهِنَّ عَلَىٰ جُيُوبِهِنَّ ۖ وَلَا يُبْدِينَ زِينَتَهُنَّ إِلَّا لِبُعُولَتِهِنَّ أَوْ آبَائِهِنَّ أَوْ آبَاءِ بُعُولَتِهِنَّ أَوْ أَبْنَائِهِنَّ أَوْ أَبْنَاءِ بُعُولَتِهِنَّ أَوْ إِخْوَانِهِنَّ أَوْ بَنِي إِخْوَانِهِنَّ أَوْ بَنِي أَخَوَاتِهِنَّ أَوْ نِسَائِهِنَّ أَوْ مَا مَلَكَتْ أَيْمَانُهُنَّ أَوِ التَّابِعِينَ غَيْرِ أُولِي الْإِرْبَةِ مِنَ الرِّجَالِ أَوِ الطِّفْلِ الَّذِينَ لَمْ يَظْهَرُوا عَلَىٰ عَوْرَاتِ النِّسَاءِ ۖ وَلَا يَضْرِبْنَ بِأَرْجُلِهِنَّ لِيُعْلَمَ مَا يُخْفِينَ مِن زِينَتِهِنَّ ۚ وَتُوبُوا إِلَى اللَّـهِ جَمِيعًا أَيُّهَ الْمُؤْمِنُونَ لَعَلَّكُمْ تُفْلِحُونَ
Translation: "Say to the believing man that they should lower their gaze and guard their modesty; that will make for greater purity for them; and Allah is well acquainted with all that they do.
And say to the believing women that they should lower their gaze and guard their modesty; And tell the believing women to reduce [some] of their vision and guard their private parts and not expose their adornment except that which [necessarily] appears thereof and to wrap [a portion of] their headcovers over their chests and not expose their adornment except to their husbands, their fathers, their husbands' fathers, their sons, their husbands' sons, their brothers, their brothers' sons, their sisters' sons, their women, that which their right hands possess, or those male attendants having no physical desire, or children who are not yet aware of the private aspects of women. And let them not stamp their feet to make known what they conceal of their adornment. And turn to Allah in repentance, all of you, O believers, that you might succeed.
Do coeducation systems in schools and other educational institutions go against the above hadith & Quranic verses?