You can, of course, write with whatever words you wish to use. If you wish to be understood, however, you will use words that other people understand as you meant them to be understood. If you use the word “he” to mean men and women, you are miscommunicating. And if you are producing a product for sale or other profit, you are losing customers and users.
The only ‘male’ word that even remotely approaches gender-neutrality is the use of ‘man’ in the sense of ‘the human race’. And even there, you’re going to be treading on irony if you use it too unquestioningly. “Man is a social animal, thought Sarah. He needs regular care and feeding.”
For more detailed information about the non-gender-neutrality of ‘he’ and such, see:
Brown, Roger, and Gilman, Albert. The pronouns of power and solidarity. In Thomas A. Sebeok (ed.), Style in Language. Cambridge, Mass.: MIT Press, 1960.
Burr, Elizabeth; Dunn, Susan; and Farquhar, Norma. Women and the language of inequality. Social Education, 1972, 36, 841-845.
Hyde, Janet Shibley. Children’s understanding of sexist language. Developmental Psychology, 1984.
Martyna, Wendy. Comprehension of the generic masculine: Inferring “she” from “he.” Paper presented at the 85th annual meeting of the American Psychological Association, San Francisco, August 1977.
For more information about gender issues in general, I recommend Sandra Bem’s “The Lenses of Gender”. Also interesting is Tavris and Wade’s “The Longest War”.