وَمِنَ النَّاسِ مَن يَتَّخِذُ مِن دُونِ اللَّهِ أَندَادًا يُحِبُّونَهُمْ كَحُبِّ اللَّهِ ۖ وَالَّذِينَ آمَنُوا أَشَدُّ حُبًّا لِّلَّهِ ۗ وَلَوْ يَرَى الَّذِينَ ظَلَمُوا إِذْ يَرَوْنَ الْعَذَابَ أَنَّ الْقُوَّةَ لِلَّهِ جَمِيعًا وَأَنَّ اللَّهَ شَدِيدُ الْعَذَابِ

Bismillah! Al Hamdulillah!
Wa AsSalatu AsSalamu A’ala Rasulallah!

So, how do people set equals with Allah?
A simple one way of understanding it is when people give the right to something/ someone else which only deserves/ belongs to Allah Subhanahu.

How do we understand it more simpler way in a regular acts?
Say, a men (husband) has a particular right over his women (wife).
This right only belong to the husband, not to any second person.

What if the wife gives the same right for 5 minutes to someone else?
As an act, She will commit a Zina. The husband will never take it easy.
But as an idea, the wife just make someone else equal to the husband.

So now, how do people make someone/ something equals to Allah?
To understand that we have to find what is Allah’s right that he doesn’t accept any share/ partner/ equal to him?

Issue no. 1:
Allah doesn’t accept a partner/ equal in regards to Ebadah.
(Sura Al-Kahf 18:110)

Issue no. 2:
Allah doesn’t accept a partner/ equal in regards to His Hukm/ Law/ Legislation.
(Sura Al-Kahf 18:26)

Now, if a Muslim obeys a law other than Allah’s law willingly, he gives those lawgivers equal status to Allah. Thus he commits Shirk and become a Mushik.

Allah knows best.
May Allah save us from engaging in Shirk by giving His right to the Kuffar by willingly obeying, submitting to the Kuffar’s law by willingly staying in the Kuffar’s lands, under the Kuffar’s authority.
Ameen.