As many people have already touched upon there are some primary reasons for the rule being in place.
1. People sometimes get it wrong: In actuality, most of the time I've seen a user tell another user for violating a rule, the backseat moderator has been wrong and the actual "infringement" wasn't against the rules. This can be very problematic ESPECIALLY if the user being told off is new, it can cause them to feel unwelcomed in the forum, can cause them to learn incorrect rules and has other unfortunate side effects. It's best that moderators step in to make sure that the appropriate rules are being followed and that the appropriate action is being taken. (And while moderators do sometimes make mistakes, we have a great team that discusses these actions in great length, so potential mistakes can be reversed and the correct action taken, something that is less viable with backseat moderators)
2. It can cause arguments: Someone who attempts to take forum justice into their own hands, even if they're correct, can cause arguments and debates that eventually spiral out of control. There are two reasons for this. The first reason is that the backseat moderator does not have any additional powers to silence a heated argument, if you tell someone to "follow the rules" and they say "No f you", there's not much you can do about it, instead what will most likely happen is there will be a heated response and the thread will spiral out of control causing a much worse situation than the initial rule infraction. The second thing is, you're just a normal member, and by telling someone to "do something" people can take offense to that, there's no reason why you should be commanding them, so they may lash out against that, feel unwelcome, annoyed or irritated at the user for trying to enforce a rule that he doesn't really have the authority to enforce.
I personally think that reminding someone that "Maybe this isn't the most appropriate of conversation", is fine. It doesn't involve a demand, it's just saying "I'm feeling uncomfortable with this, so please stop" and that's totally fine. But telling someone to "Follow the rules" or "You're doing X wrong you should do Y" can be problematic due to the above reasons.