Chivalry or Ego?

Women of this community, recently I've been thinking, when does chivalry from men feel genuine and respectful? And when does it come across as male ego? Suppose, opening the car's door for her, recently, while commuting home from coaching, the cab driver picked another girl to drop her off, and when she was stepping out, I opened the door for her and handed her bag, earning a cough and a disgusting look from another girl sitting beside me, and has me wondering where did i go wrong? Did it come across as a display of male ego? How come? My intentions were genuine. And, in what situations do women appreciate chivalry?