Specifically.
If the oil isn't the sole reason we have to invade, what is(are) the reason(s)?
Once they're stated, it shouldn't be hard to find other countries doing exactly the same thing WITHOUT the oil that we aren't talking about invading.
Therefore, it is about the oil. Without the oil, no talk of invasion. With the oil, invasion.
No oil == no invasion
oil == invasion
Tack on whatever additional items you want. That basic equation will not change.