Different words.

There are Iraqis who want a foreign invader out of their country. (I think we'd agree on that.)

These Iraqis don't want an Iraqi government which is an arm and agent of the foreign invader. The Iraqis are aware that a substantial number of the government officials have been CIA employees. (Nothing controversial here.)

The Iraqi population supports these nationalistic Iraqis to the extent that the Iraqis are able to sustain a guerilla war against the foreign invaders and the puppet government. (That's obvious.)

The foreign invader has to maintain a large military force to keep the foreigners hand-picked government in place. (Again, obvious.)

Because if it were up to the Iraqis themselves the government would be overthrown. (QED)

Therefore, the government which was installed by the foreign invader isn't all that popular. (Reasonable conclusion.)

So far, so good?

Arf

PPS Regarding killing Iraqis. The foreign invader has been killing Iraqis who want the foreigners out. Lots of Iraqis.