the issue isn't to do with the placement of the model

the reason why your model isn't going to cut in half is because you're model doesn't have a line down the halfway point

you see in your polygon model you have a giant triangle strip? you can't delete half of it if there are no edges on the halfway line

however, your head is ok. it has edges along the halfway mark

this is a problem with your conversion from NURBS to polys. try different conversion parameters when you click the option box next to convert > NURBS to polygons... also, when you convert you should convert as quads, not triangles.

you can still play with the conversion parameters after you've converted if you have construction history enabled

some of your edges look like they are already on the halfway line of the model, so what you can do is use the split polygon tool to draw in the edges that would enable you to properly delete half of the model



also, this may sound a little harsh but in future please title your posts properly. titles that have the phrase "help me please" (or similar) in them shows people you haven't actually thought about your problem. Although this may be untrue for you being new to maya and probably the concepts of 3D