While one should certainly never be embarrassed about any halacha, it is not a good idea to make a point of quoting something that he knows will be misunderstood and lead people to have incorrect ideas about Judaism and the Torah.
The above halacha is a halacha whose intent could be misunderstood by many as meaning that women are not as valuable/important as men. Those of us who have been learning and living Torah our entire lives know that that can not possibly be the meaning of that halacha, and therefore are not disturbed by it.
However, someone who has not been living and learning Torah his entire life would assume that is the meaning of the halacha, if it’s not explained properly. And since it is part of a very complex and vast topic, it is unlikely that anyone here would be able to explain the halacha properly in one post of less than 1,000 words (or whatever the limit is). This is particularly so given the misconceptions prevalent in today’s society regarding women and men’s roles and the concepts of equality and different roles in general.