Pure Friendship between Men and Women

Whether there is pure friendship between men and women?
In order to discuss this issue, there are two definitions that must be clearly defined, the first one is the definition of a man and a woman, and the second is the definition of friendship.
What is the pure friendship?
When a friendship has no other underlying reason or purpose to be understanding and respect – it is pure friendship which is a form of relationship that will not constraint or burdens each other.

Whether there is pure friendship between men and women? If you want to be close to a friend, I don't think there is pure relationship between them! Except for those who are just ordinary friends. Attraction between men and women begins with the interest, this kind of attraction is like the earth and the moon, so a boy will become friend with a woman because of the interest, and once the woman has strong interest to the man too, both of them will be stay together naturally .I believe that our early ancestors are having more sexual life compare to our generation, hence they are having higher risk of getting sexually transmitted diseases. Following the continuous evolution, as people having wisdom, they will think of ways to prevent sexual promiscuity, therefore there is a good excuse to refuse sex by becoming friend.
I never believe that men and women can have the pure friendship, perhaps women are more rational, and believe to be well-controlled in their mind, but men are different, they will having imagination in all the time, this is unavoidable. Even if there is, it can only be controlled at the beginning stage, after that this kind of feeling will be change. When a man starts to concern to a woman, observing her emotions, spending a lot of time to accompany her, then this kind "friendship" is considered as the beginning of pursuing of love. Rational thinking of man makes them to be strong when doing something, if it is not what he expected; he won’t spend a lot of time and effort on it. Therefore, many women consider a man is her good friend and good brothers, but this kind of relationship slowly changing between them, and thus lead to feeling worried.
I have a male friend -- David, who told me that he met a pretty girl through the internet. At first, the relationship between them was just a pure friendship, but while they are chatting through the Internet, the girl will give him a hint from time to time, seem like hoping that David to aspire her, very ambiguous between them. However, when David expressed that he has fallen in love to her, she replied that: we said that before we are only be good friend, right? I don't want to loss as good friend like you, I hope that we are just good friends forever.
After this incident, I found that when standing on a woman position, it is believed to have the so-called pure friendship between men and women. This is because the more of her male friends, the more people will take care of her. In order to fawn the woman, a man will ask her to dinner, buy her some small gift, chatting with her when she is bored and listen to her complains, so many benefits, which woman will refuse? So woman wish to have many men only to treat her as a pure friendship, if she has no love to them, she also hope that these men would be the friends who can always accompany her, even if she failed love, the men are still beside her, waiting for her to talk about her pain, as long as she has a hard time, those men will appear around her, comfort her, pity her, persuade her, convince her, take care her and so on.
Consequently, we can conclude that men and women have almost no possibility to have pure friendship, even at the beginning they successfully maintain the pure friendship, but in progression of time, there may no more pure friendship.