1. They are usually just bluffing to try to make somebody give them what they want. Most of the time they are spineless little shits who won't actually risk doing anything in-game to get themselves banned.
2. They lose LP if no one trades with them, so they're even more likely to dodge than you are. Simple as that, if they screw themselves and their team by taking a troll-pick or doubling up on a position with an ally, they suffer the consequences too. And they don't want those consequences, otherwise they wouldn't be playing ranked.
3. Dodging or giving in to a demanded role swap reinforces their bad behavior and will make them more likely to do it in the future. Don't give them the satisfaction. Don't help them.
4. Dodges are already really limited. That player can't afford to dodge frequently. Which is why they are trying to force you to do it instead of them. If you do not comply, then they are forced to use their dodge and risk facing a queue penalty. Their dodges are a lot more limited than you think. And you can stop their bad behavior dead in its tracks if you force them to give up their own dodge.
#Join the cause. Stop the hostage takers. Together we can put the little shitlets in their places.
_EDIT 1: Credit goes to SanKakU for inspiring me to write this post in the first place._