You said that, after passing the bike, you both came up at a red light. Like this:
In Fig. 1, Dan is behind Bike Guy. Then, in Fig. 2, Dan did a seemingly reasonable thing and passed Bike Guy, who was going pretty slow. However, then they both came to the red light in Fig. 3. Like any normal human, Bike Guy came up alongside or slightly in front of the car. (Unlike a normal human, he also went nuts.)
The thing is that, after the light turns green and you both go (Fig. 4), Dan just needs to pass Bike Guy again (Fig. 5). This can be kind of frustrating as a cyclist: when a car passes you, only to get into a situation where they’ll need to pass you again!
The alternate strategy is to stay behind Bike Guy: essentially to skip Fig. 2 and go straight from Fig. 1 to Fig. 3. You reduce the total number of passings from 3 to 1! And you both get where you’re going at the same speed, because the light is red anyway.