I've been asked as to whether an Earth Elemental can carry people while burrowing underground, using Earth Glide?

After reading the creature's abilities, my answer is no. The way I understand it, they burrow through the earth using Earth Glide at a speed of 30ft. (Their burrow speed is dependent on using Earth Glide, as far as I'm concerned). But Earth Glide means that "Earth elementals glide through rock and earth as though they were liquid".

If they're carrying anyone they'd die from being suffocated (assuming the carried being need to breathe), or merge with the earth in an unpleasant way for them,  and then die from that.

Can an earth elemental even drag someone underground? After looking at their abilities, Earth Glide abilities only seem to apply to them alone so I'd say no to that as well.

Opinions? 

No. Earth glide doesn't disturb the earth at all so there is no hole or anything for a creature being carried to exist in and it would be way too harsh to sufficate a creature because it was grappled by an earth elemental 

but an earth elemental COULD* be waiting underground, then reach its arms up and pull a target SLIGHTLY into the ground, effectively removing them from combat. I wouldn't do this unless you want to really be mean

*well, I would allow it

Allowing the elemental to pull people halfway into the earth is more Over Powered than letting them transport stuff totally through.

The elemental can move through the earth but cannot pull a creature through it a single centimeter. 

It is like a ghost, the ghost can move through walls, it cannot pull you half way through a wall anymore than they could pull you all the way through.

Thanks for all the responses everyone, they've been very helpful.

I told the player no, and he's picking something else. 

Just to play devil's advocate, I think you could interpret Earth Glide as earth parting around the elemental and then returning to its original position rather than phasing like a ghost. I don't see why it couldn't hold someone against its body and part the earth around the both of them.