Is woman a worrying man?

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I read a lot of books in history, politics, literatures and more and I noticed one thing- when the author wrote the word "Man" for example "when the man begins to wonder..." the author means to include in the word "man" the woman but he simply used the term "man". In another situation, some mentioned "Mankind" which refers to both man and woman of the earth but only uses the word "man". I wonder why, man is solely used to denote man and woman. In one occasion in my classroom when I was teaching history subject, I started the lesson like this- "All right class, now let's study the history of man.." suddenly a lady rose from her chair, raised her hand and registered her strong comment to my subject matter, thus she spoke- "I disagree sir, how about the woman" she said. since then, I made my own research on the matter. I ask many experts on the subject matter and one of my friend has a very near explanation on it, which according to him, the root word of the term "woman" is "man". The woman was called "woman" because she is a man who is always worrying for everything, a woman generally is worried on anything else, she has many if in life, thus the supposed term of a woman is "worried man" and it was shorten to single word as "WOman". Can you please lighten me on this subject? Is it true that a woman is always worrying for anything else, hence she become woman?