The English language indeed has an inherent gender bias, particularly in the habitual use of the male pronouns “he,” “him,” and “his” when the antecedent is a noun of indefinite gender, as in “A trustworthy lawyer is he who respects confidences,” or an indefinite pronoun like “everyone” or “everybody,” as in “Everyone is entitled to his opinion.” The easy way out is, of course, to use the “he or she” form, as in “A trustworthy lawyer is he or she who respects confidences,” or the “his or her” form, as in “Everyone is entitled to his or her opinion.” This is fine if you will use the “he or she” form or “his or her” form only once or at most twice in a typical page of written work, but it could grate on the reader's nerves when repeated several times.
I must tell you frankly, though, that you would be gender-biased yourself in favor of women—and deserve to get that “you-must-be-a-feminist” stare—if you habitually use the “she” or “her” form when referring to antecedents of indefinite gender, as in “A trustworthy lawyer is she who respects confidences” and “Everyone is entitled to her opinion.” Both forms do look and sound like you’re rubbing it in against men, so I would suggest that you confine such usage when you’re in the presence or company of an all-female group like, say, the Women Lawyers League.
A much better and more politic way of dealing with gender bias is to avoid it in your writing and speech as best you can. For the same situations in the sentences given as examples above, in particular, you can:
1. Use “one” instead of “he” or “she”: “A trustworthy lawyer is one who respects confidences.” Or pluralize the antecedent noun to avoid making a gender choice: “Trustworthy lawyers are they who respect confidences.”
2. Pluralize the antecedent indefinite pronoun to avoid making a gender choice: “All are entitled to their opinion.”
One more thing: You need to be extra sensitive to the need to avoid gender bias even in less obviously gender-skewed sentence constructions. For example, you need to cultivate the art of avoiding writing or saying, “Everybody is enjoined to bring his wife to the club picnic this weekend.” The gender-bias-free construction for that sentence is, of course, “All are enjoined to bring their spouses to the club picnic this weekend.”