That last bit is where many men tend to miss the mark.
Let me give you probably the most extreme example widely known in narrative form.
“Hello there. I see you’re a woman and I was taught to be a gentleman. Let me get that door for you. Now that I have demonstrated to you my chivalry, I’m going to murder you, chop you up into pieces (not necessarily in that order) and leave your body parts in the woods.” — Ted Bundy