Public service announcement: I am trying to explain. Please respect the implicit ratio of explanation :-) Try to understand, do not look at these as points which you should argue about. Unless you wish to offer alternative explanations :-)

It would only appear as if the enlightened worldview is superior to the mythical. In reality, both approaches would be closely connected.

Would, according to H&A. I struggle with tranlating the konjunktiv. This part should be relatively clear, otherwise. Instead of opposition, there is connection.

The ideal of enlightenment is the rational explanation of the world in order to control nature. In it, understanding is replaced by the formula.

What H&A are saying is that enlightenment implies a striving to instrumentalise our grasp of nature, so that it can be used for controlling nature. This is exemplified by the formula (quantitative research). By understanding, they presumably mean a grasp of nature that is an expression of our interrelation with it.

Through the argumented defense of the mythical interpretation of the world, the principle of rationality would already be acknowledged. As a result, it would get stronger with each confrontation.

Here H&A are saying that rationality and myth have different rationalities, basically, although we perhaps should not think of myth as having a rationality, strictly speaking. But by trying to defend myth through rational argument, you have already ceded the ground. Unless you transcend that mode of argumentation, like rg regularly manages :-)

We show, do not explain. But I have not mastered that allusive language yet!

"As being and an event, enlightenment only recognises that which can be encompassed in the unit; its ideal is the system, from which all and everything follows."

I actually mistranslated this quote (slightly): instead of 'the unit', I wrote 'an event'. Not too dramatic in terms of meaning, but the sentence looks better now. "Was durch Einheit sich erfassen last" can also be translated as "what can be compassed through unitariness". If you are familiar with anti-foundational criticism, you might see where this is headed. Instead of criticising a copernican point from which things can be developed, H&A criticise the system which seeks to define everything as points; units.

All gods and qualities should be destroyed.

I'll refer to ChrisCook's diary here.

In this, it overlooks that myths are already a product of the enlightenment. "As commander over nature, the creative God and the ordering intellect are alike."

This is best understood by the allegory of the Greek gods, standing on Mount Olympus and looking at the world, fixating everything with their gaze. In their eyes was the determinate definition of reality as it really is. The ordering intellect seeks to make itself external to reality in order to determine, to attain the view of the gods, in turn, according to H&A, to then have the power of the gods.

They have the same roots, as "myths like magical rites hold themselves to have a repetitive nature."

Here I think H&A state that science has ritual elements (for instance, the eternal cycle of impovement) at its roots. This is a bit thin, so you should perhaps conceive of it more as an overtone or colour in the origin.