Who Should Make the First Introduction?

When making an introduction, introduce the person who is being presented last. Also, keep in mind that social etiquette is based on chivalry, so in a social situation we defer to people based on gender and age by introducing women first and then those oldest. Business etiquette is different because it is based on hierarchy. Gender and age play no role, but rank and authority do.
The rule is that people of lesser authority are introduced to people of greater authority:
“Mr./Ms. CEO, I would like to introduce Mr./Ms. Junior Executive.” Again, remember eye contact. Look at and speak to the greater authority first; look at and speak to the lesser authority second.