(Dengekionline) Preview for patch 3.2.

[Lunaxia]

Because they're the only class that really uses Ice in any significant way. NIN does have an Ice spell, but it's essentially never used, and Shiva is presented as a caster in battle that wields powerful Ice magicks. The closest thing to that among the classes/jobs is THM/BLM. I mean, yes, they could have given caster the Ramuh set just as well (or the Ifrit one), but that would then require shuffling the other classes around.

They're also the only class that uses fire/ lightning in any significant way... and all the primals are "casters that use powerful (element) magicks", Shiva is no different. Well, actually, she is, in that she swaps weapons to a sword and bow as well as wielding magic. You could argue why not a Shiva PLD/ BRD instead with that logic.

It's an odd choice combat-wise as well as stylistically.

[Alahra]

They're also the only class that uses fire/ lightning in any significant way...

The difference though is that the other classes overlap to some degree with the other primals in other ways. Ifrit fights primarily with his claws and also dashes around on the ground—similar in many ways to PGL/MNK. Garuda is heavily associated with the sky, just like LNC/DRG, and so on.

I do agree that the caster set could have been Ramuh, but given Ramuh's association with the Shroud and the Sylphs, which are rather closely tied to Conjury and White Magic, healer is the more likely thematic choice for him.

It's not just the fact that Shiva uses Ice magic that made it their choice for caster. It probably also has a lot to do with Shiva fitting less well with the other classes, and since BLMs use Ice magic, it was the simplest fit.

Your association of Ice with healing doesn't even really build off of much in game—the elements of Conjury are Earth, Air, and Water. Ice is specifically associated with destructive (i.e., Black) magic in the game itself. The three healing classes have no association with Ice in the game, whereas THM/BLM does have some.