I'm not saying it's pretty but by refusing to sell us oil they effectively kill us.

Lets for the sake of simple maths say the middle east is 25% of the world and the rest is 75%. Then change oil for drinkable water as this is easier to understand. Say they owned 75% of the worlds drinking water and the rest of the world had to survive off a 25%. The rest of the world pays to use this water but suddenly the region decides they aren't going to sell it any more. Suddenly the rest of the world doesn't have enough drink water for everyone and has no way of getting more. Would it then be reasonable to invade this 25% of the world so everyone had enough to drink? Or change oil/water for food which is essentially the problem. Oil has the same effect. Without it a large proportion of the western world starves and dies, we wouldn't be able to sustain the current population without advanced agriculture which currently is highly dependent upon oil to do so.

What if a stable democracy decides, for whatever reason, not to sell oil to the west anymore despite being a major source.

Then we still have to fight for it, the stability of the goverement only matters as an unstable region is near impossible to trade with whilst most stable nations will trade what they have a surplus of for things they need but don't have.

And if the atrocities of the given dictatorship are such a major factor then why aren't we invading any unstable country plagued by frequent atrocities? Africa is full of them.

It is indeed and maybe the world should wake up and care about that but it is an entirely different argument. Iraq was unstable, likely to go into revolution thus potentially destabilising the entire region. This could stop the oil flow so we went in. As I explained above, no oil and the west rapidly falls apart and many people die. Africa doesn't have anything the rest of the world needs so desperately so it gets ignored. Whether ignoring Africa is right or not is entirely separate to the need to fight for oil