By experience and observation, I can prove that coeducation is better. Our school is coed. Its the best, in terms of academic performance in the country. Other comparable schools are the same. If your assumptions were true, this wouldn't be the case.
We don't need to hire boys and girls from other schools for cultural performances, unlike the single sexed schools.
Everybody will agree (even male or female chauvinists) that seeing the same faces everyday will be very boring.
When the subject of coed comes up, what immediately enters their mind in the first place, is sexual relationships between students. They fail to see the many advantages. Even this phenomenon is a good advantage as it teaches boys and girls to control themselves (most of them learn to, except a very few minority), which they would not learn in a single sexed school.
For those who think this way, thus, boys and girls from single sexed schools, in fact, has a higher chance of becoming sexual beasts attributed to crimes like rap*, molestation or even prostitution simply because they do not learn to control themselves and the other sex is such a 'mystery' to them. It is always a characteristic of human to try to explore the 'unknown'. Students from coed schools, for the vast majority, learn to control themselves, for which they are undoubtedly better in coping with any situation, in their future life.