Did they say that (in some sort of chat) or was that the reason they picked from the menu (you need to pick a reason why you want to dismiss someone)?
If it was the first one and they did kick you for "cheating", it might very well be that they noticed something that seemed odd to them but had other reasons than cheating - for example: you could have been teleporting through the dungeon because of lag but to them it could also have looked like you were using some sort of cheat (when you actually wasnt). So they might have truely believed that you were using some kind of hack or cheat and removed you because of that.
Its also worth noticing that "Cheating" isnt the same in every language - in german that option translates closer to "Illicit activties" (Unerlaubte Aktivitäten), which opens up a broader interpretation.
If it was the later: While "difference in playstyle" is a valid reason to remove someone from a dungeon, we dont have that option directly so people usually just pick anyone from the list.
You can report them for kicking you, but unless they outright said (in chat) that they would remove you to mess with you or insulted you in any way the GMs wont do anything about it, since kicking for difference in playstyle is okay.
While I understand that being kicked is upsetting, it would be intresting to get more context.
What duty? What class were you playing? Was that class geared properly and were you using proper rotations (you'll be "doing damage" even without proper gear and rotation, thats why I'm asking)?
They might have had a reason why they didnt want to continue playing with you - and you're just not aware of that reason. Bad gear and lack of knowledge in terms of general mechanics and job performance are the usual suspects.
This still doesnt like something to quit the game over. Two people didnt want to play it with you, so what? That doesnt change any of the content, nor does it change any of the content you were looking forward to - forward enough to pre-order an expansion you cant even access because your character hasnt finished Stormblood yet...?