Will all three parties involved (you, your husband and the contractor) be very upset if I said that neither approach is correct?
Well, let me back it up a bit: how many walls are you tiling, two or three? If you have two walls to tile (and the rest is glass), I would tend to agree with the contractor - wrapping (or using the rest of the tile which has been cut to size for the adjoining wall) makes sense - less waste and will not look off.
But if you are tiling three walls, they are all laid out differently and most likely no layout would allow for exactly wrapping or mirroring. The tiles on the central (back) wall are usually laid out so that a center of a tile coincides with the half-width mark on the wall unless that will make the edge tiles less than 1/3rd of their normal width, in which case you just start with a full tile in the corner and then the center will be slightly off but not noticeable. So, the edge tiles on both left and right are cut to the width that makes center of one of the tiles arrive at the middle of the wall, and that has nothing to do with the side wall tiles' width.
The side wall tiles usually start with full tiles right at the outer trim (or just the outer edge) and work toward the back wall, so they arrive at the back wall at a certain width of the last column that is not exactly correlated to the width of the first tile on the back wall - so it's neither really wrapping nor mirroring, the widths of the last tile and the first tile on the adjacent wall are depended mostly on the length of your walls.Â
This assumes that these are tiles without a particularly large pattern which may make the entire job a custom layout in which case I would recommend listening to what your contractor has to say. They've likely laid it out, perhaps even using a specialized software on a computer, before commencing the job and if wrapping makes the pattern look especially pretty, then wrapping it is.