P-channel MOSFET high side switching, Arduino 5V pin and Vcc connection
Based on your clarifying comment after your posted question, I think that what you are asking is why you can't connect this differently, so that instead of tying the +5V and the +12V lines together, you tie the grounds together, and then just drive the MOSFET gate with the Arduino HIGH or LOW output.

If that understanding of your question is correct, then the answer is that the MOSFET will never be turned off, because the source terminal will be at +12V and the gate terminal will be at +5V at the highest. So you will have at -7 Volt Gate-Source voltage even when you are trying to turn off the MOSFET, and it will always be on.