The question is why is it so bad? I think there are plenty of sins against God Himself that are worse than polytheism like committing evil act in His name for personal gain, Atheism, or Satan-worshiping acts. What sets polytheism apart from any other sin?
Shirk means "associating partners with God". The "partners" can mean anything, literally, anything. To attribute something that belongs to God to something else, whether it be an animal, an object, a person, or an action, that is associating partners with God. Polytheism is merely another form of Shirk.
Some examples of Shirk:
-Saying you are better than God
-Believing that the stars have effects on the daily things that happen to us in life. So, astrology is full of Shirk then
-Believing you don't need God, because science explains everything, thus God has no part. This is Shirk as well.
-etc.
Why is Shirk so bad apart from all other sins? There are two types of deeds that all people do, for humanity, or for God. We are also humans ourselves, so if we do acts for ourselves that comes under humanity. You can wrong yourself, but that is yourself. God can always forgive you for what you do to yourself. He made us. If we do a wrong to someone else, we wronged that other person. This forgiveness requires some action of forgiveness from the other person, or some kind of suffering in this life or the hereafter. That is how wrongs against other people are dealt with. In fact, punishment works for ourselves as well.
But when it comes to God Himself, the Highest Being in the universe, the One Who created everything, even us and all of creation, the King of all kings, the Master of the universe, etc., you better believe that giving any rights that belong to Him to someone else is a grave wrong. Shirk involves the belief in something other than God with those same Godly attributes and traits. We were created to worship God, that is the very purpose of our existence. So when we go against that purpose and start doing something contrary to it, then this is an affront to God.
The only way to fully grasp the concept of attributing partners with God, from the Islamic perspective, you would have to study the concept of God in Islam, by understanding the attributes and the rights due to God.
In the end, what is worse, going against the All-Powerful God, or against a human?