Gender Equality-The double standard

Many countries around the world past and present have campaigned for gender equality. They campaign that women should be allowed to join the army, vote and drive cars. However, despite this, men are still required to give way or give up seats  to women. The reason for this is because many consider women to be the "weaker" gender. But isn't this a double standard? If women strive to be equal to men, shouldn't they at least stand like men do since genders must be equal?