Why can't I run a mac program natively on windows?
Think of the .dmg file as a book of short stories.

Windows and Mac OS X have different formats of books, so the gesture to open one is a bit different (think of pages turned from left to right or right to left). Less metaphorically, a .dmg file packs a bunch of files, and the format in which these files are packed isn't one that Windows supports natively. However it would be easy to write a program to unpack .dmg files on Windows, and I'm sure someone has done so.

Ok, now you have the book open and can see the pages. That doesn't necessarily mean you can read it, though. Let's say you speak English and only English… but the book is in Turkish. You aren't going to be able to understand a word of it.

A computer program contains a bunch of elementary instructions. The instruction set is like the script that the book is written in. The instruction set is determined by the type of processor that powers the computer. Modern Macs and Windows PCs have the same type of processor (one of the two x86 families, either the 32-bit one or the 64-bit one). So that step is fine — you can make out the individual letters. However, that's not enough!

Some instructions rely only on the processor: instructions like “read the value at this memory location” or “add these two numbers” or “jump to this location in the program”. However, every time the program wants to interact with something else (access a disk file, read user input, display something, communicate over the network, etc.), the program makes a call to the operating system. And two completely different operating systems, such as Windows and Mac OS X, have completely different APIs — they offer completely different system calls. (Note that the metaphor breaks down somewhat here: the problem isn't that the arrangement of instructions has to be different, but that a few very important instructions have radically different effects.)

There's even another layer of differences: Windows and OSX even have different executable file formats (PE vs Mach-O). The executable format determines how code and data are arranged in the file and how things like dependencies on libraries are represented. Making Windows understand OSX's file format would require some work, but making Windows understand OSX's system calls would be a Herculean task.

You can't read the book because it's in Turkish. You could learn Turkish, but it would take years of effort. Similarly, making Windows able to run OSX programs would take a huge amount of programming effort.

In fact, it's simpler to simulate a processor with its peripherals, by implementing all of its instructions, than it is to simulate an operating system by implementing all of its system calls. This is called a virtual machine. You can run an operating system on an emulated machine that is in fact provided by a program running under another operating system. For example, you can run OSX on an x86 CPU emulated by Vmware which is running as a Windows application. (In the specific case of OSX, this is difficult, but not for technical reasons, rather because Apple makes it difficult for commercial reasons.)