Incoming wall of text. Meant to reply to some of this stuff earlier, but got caught up with stuff and forgot about it. :v
I just want to point out, with regards to Destatiredux's example, he was talking about a Level 70 dungeon (Temple of the Fist). People should not be teaching the very basics of a job to someone who is at endgame. The rotation of using Fire spells until you don't have enough MP for any more, switching to Blizzard until full MP, and then switching back to Fire spells is the foundation of a BLM's rotation and extremely basic, not spamming Thunder on mobs. People should not be having to teach that to BLM's that are running level 70 Expert Roulette dungeons. And this goes for any job as well. It's a little different if they had been telling him how to use newer Stormblood skills, or fitting together a more optimal rotation for level 70 using said level 70 skills, but not for what Destatiredux pointed out. When a BLM reaches level 70, they should most definitely know how counterproductive it is to spam a single spell such as Thunder or Blizzard (though this is sadly not the case with quite a few of them, and really, a BLM should know by level 10 not to just spam a singular spell). Doesn't help that the BLM in question sounded like they responded with hostility when questioned why they were just spamming Thunder spells and not touching fire or ice spells. Hostility makes it less likely people will want to help someone, since the person in question probably wouldn't listen to the advice given anyways.
And that's fine, but you still seem relatively new to this game, and it is surprising the amount of players you will meet in endgame content (and I'm not talking about just Expert Roulette dungeons, but Savage and Ex primals as well) that don't know the basics of their job and, quite frankly, don't really care to learn. There are, sadly, individuals out there that are perfectly okay with performing sub-optimally, and allowing the other 3/7/23 people in their party/raid/alliance carry them while they do next to nothing. I honestly don't have any trouble believing the Thunder Mage story because it's already common enough seeing Ice Mages, or poor DPS that don't want to AOE large trash packs, don't use the very basic self-buffs of their jobs (looking at you, DRGs that don't use Heavy Thrust or BRDs that don't upkeep Straight Shot), etc.. Which is an extremely sad state of affairs, but if people aren't willing to listen to advice or constructive criticism and willingly improve, then there isn't anything that can be done about it.
I'm all for helping people and extending advice on how to play jobs that I know inside and out optimally, or how to do a certain fight/handle certain mechanics, but I won't waste my breath on an individual that is reluctant to even listen, and reluctant to learn. And I most certainly won't waste my breath on people who are rude for no reason when you're trying to help them.
It's actually very easy to pay attention to individual's rotations in a duty. When I notice that things are taking longer than they should to die, I start looking at the DPS in the party and see what they're doing wrong. Example: tank does the huge first pull in one of the level 70 endgame dungeons, and they're taking an extremely long time to die, even though I am AOEing my heart out. Glance over at the DPS and see them sitting at full TP (melee/physical ranged) or full MP (casters), then I can very easily tell that they are single-targeting, and not using their AOE combos to make things go down faster. Zeroing in on the cast bars in the party list isn't exactly difficult to do either, for those who are casters (I have a tendency to watch other RDMs that I run with to see if they actually use Scatter for large pulls--quite a few of them continue to just single target Ver spell things).
It isn't always about "Well, we didn't wipe, so it's okay." I honestly dislike this mentality, because just because a party didn't wipe doesn't mean that it makes suboptimal play or behavior right. I could queue into an 8-man raid or Ex trial on my AST, and proceed to strictly DPS only, not help heal, not help raise, not draw cards, etc.. But just because my party does not wipe does not mean that my play was optimal or considerate to the group, especially the other healer. These parties and duties are team efforts, and if a player isn't willing to play in such a way that is beneficial to their team, then they don't have any place in that party.
With regards to Vote Dismissing, majority rules in a party. If you (using general "you" here), were kicked from a 4-man party, at least 1 other person aside from the individual initiating the kick agreed that kicking you was a viable option. If you were kicked from an 8-man party (be it from an 8-man raid or a 24-man alliance raid), then at least 3 other people decided you were a burden to the group. This logic also applies to speedrunning versus taking it slow: if the majority of the party are in agreement that one or the other is what they want to do, and there is 1 person who is reluctant to do what the majority want, unless that person is someone who is completely new to the dungeon (new tank or new healer, since new DPS don't have as much responsibility compared to those two roles with regards to the flow of a dungeon), majority decides. If the majority decides to kick the reluctant player, then it's not an abuse of the Vote Dismiss feature.
The only time I consider a Vote Dismiss abuse is if there is conspiracy by a pre-made to kick a player just because they can do so. I do not consider 3 people deciding to kick a sub-optimal player that is reluctant to listen to advice, reluctant to improve, and responding with nothing but hostility an abuse of the feature.