This is a really dense subject that you can't just "skim" so I suggest giving it a good read. I will say this though, I don't have to prove good and evil, right and wrong, etc. exist at all. You already believe it. Watch:

[The Middle East] restricts freedom of speech, womens rights, and so on.

So what? Who cares about autonomy, liberty and freedom of speech? If there is no right and wrong, then you wanting to uphold those values is completely arbitrary. You seem to value objective, absolute truths, I presume? So let's throw away these values since they have no grounding in reality and truth. But you don't. So surely you can't think that way so you must place at least some value on ideal that are beneficial for humanity as a whole (a). Social constructs can't be entirely useless(b).

So once we admit that you care about things that exist solely within the scope of humanity, i.e. social constructs (b) then it's fair to say that you value what's best for humanity (a) (or, hell, just yourself if you wanna go that route). So now we've established: (1) you have values and (2) those values are either what you think is best for humanity or yourself. That means, any action that aligns up with your value is a good action.

You might say, "my definition the goal is just my opinion and doesn't make it objectively the right goal." Sure. You're absolutely right, but at the very least you have admitted to saying that a goal, and therefore good/bad actions which are measured against it, exists and you have reasons for choosing that good over another. Thus you do believe that a good and bad exist, regardless of whether you think that good is the right one.