Regional FlagWhy dismount when taking some quests?Source
Target Source
#1 - 2019/08/14 05:25:31 PM

why cannot i stay mounted?

Target Source
#3 - 2019/08/15 12:18:22 PM

In most cases you should not be dismounted indeed. The game will however still dismount you when you interact with the game objects (not NPCs).
Some examples would be Deepflame Campfire and Calling Conch that you use to select your ally in Nazjatar, or Bounty Board used to start some of the bounty quests.
You would also be dismounted in areas around key quest NPCs, yet in that case it would be area around, not the interaction with this particular NPC.
If you would encounter situation that would not fall under the above, feel free to report it in game (Esc -> Help -> Submit Bug).