Why am I unable to delete vertices? I've got a ship model


For the purpose of a simplified collision model (My archers won't be running into the sails), I would like to remove all the sails, the rigging, and the strings. However, that does not seem to be possible.

Pressing X and going "Delete" leaves me with this:

And for some reason, the rigging won't go away.

Here's a quick GIF:



And here's a link to a less-jumpy MP4:
http://i.gyazo.com/ec063d07a527f86f592495dea173bb15.mp4

Even if I select a SINGLE VERTEX, it won't delete!

http://i.gyazo.com/a863b11ce9e9f01fcc4a77297983e2ce.mp4

How can I delete these vertices?
Blender is deleting all the selected vertices, but not all the vertices you want to delete are being selected.

This is because by default blender will not select vertices hidden behind other geometry when using a selection tool like Lasso or Box. To select all geometry including vertices obscured behind other geometry, either perform the selecting in Wireframe view (Z):



Or turn off Limit selection to visible in 3D view > Header to select obscured geometry in solid view: