Do you know what this kind of thinking leads to?
If everyone thinks "I want to give someone else a chance to pray", no one prays.
If everyone thinks "I want to give someone else a chance to experience the mission trip", there is no mission trip.
If everyone thinks "I want to give someone else a chance to go to that dinner so I'll give up my spot", there is no dinner.
At FIRE & WATER sometimes we have Scripture on the screen and I always let a student read it. A while ago a few students really wanted to do it so they started scrambling to be first to read. You know what it led to? More people scrambling to be the first to read. One time the entire group just read it in unison because they couldn't figure out who read it first and no one wanted to give up the opportunity to read.
If you really want to give someone else the chance to be a part of something, don't step back and give them the example of not doing it. Give the example of being excited and being a part, that's more likely to get others involved and being a part of whatever is going on.