Associating with Allah (Al-Shirk, polytheism):

Al-Shirk, polytheism, implies ascribing partners to Allah or ascribing divine attributes to others besides Allah and believing that the source of power, harm and blessings comes from another besides Allah. And this is the essence of Messengers' message that to serve all this attributes to Allah and only Allah Alone. Allah the Almighty said:

<< And Verily, We sent among every Ummah (community, nation) a Messenger (proclaiming): Worship Allah (Alone) and avoid (or keep away from) Taghut (all false deities etc. i.e. do not worship Taghuts besides Allah). >> (Surah 16:36)

Al-Shirk, Polytheism, is unforgivable for Allah the Exalted said:

<< Verily, Allah forgives not that partners should be set up with Him in worship, but He forgives except that ( anything else) to whom He pleases, and whoever sets up partners with Allah in worship, he has indeed invented a tremendous sin >> (Surah 4:48)

So the first condition for a person to embrace Islam is to testify: La Ilah Ill Allah (no one has the right to be worshiped but Allah) wa anna Muhammad-ar-Rasul Allah (Muhammad is Allah's Messenger).

What happened is that some nations try to assign a partner to Allah or try to explain or relate something in the universe according to their limit thinking. For example, the Arab pagans said that angels are the daughters of Allah. Also they said that Allah has a kinship between Him and the Jinn, Praise Be to Allah. Allah the Almighty said:

<< Now ask them (O Muhammad): "Are there (only) daughters for you Lord and sons for them?" Or did We create the angels females while they were witnesses?

Verily, it is of their falsehood that they (Quraish pagans) say: "Allah has begotten off-spring or children (i.e. angels are the daughters of Allah)" And, verily, they are liers!

Has He (then) chosen daughters rather than sons? What is the matter with you? How do you decide? Will you not then remember? Or is there for you a plain authority? Then bring you Book if you are truthful!

And they have invented a kinship between Him and the Jinn, but the Jinn know well that they have indeed to appear (before Him) (i.e. they will be brought for accounts)

Glorified be Allah! (He is free) from what they attribute unto Him! Except the slaves of Allah, whom He chooses (for His Mercy i.e. true believers of Islamic Monotheism who do ` not attribute false things unto Allah.) >> (Surah 37: 149-160)

Also, the Arab pagan worshiped idols and serve all Allah's Attributes to them. They said that we, Arab pagan, knew Allah but these idols were only to make us nearer to Allah. And they began to sacrifice to them and do all the things (e.g. asking for help, children, fear, love, etc.) they should do for Allah (Alone). That was against all Messengers' (peace be upon them) call that is La Ilaha Ill Allah (none has the right to be worshiped but Allah)

Arab pagans (Quraish) are illiterate and arrogant. But how about the people who know Allah best and some of the Heaven's Knowledge. That is the people of the books (Jews and Christians).

The people of the books (Jews and Christians) say that Allah has a son and we are Allah's children, Allah Be Praised Above All. Allah the Exalted says:

<< And the Jews say: Ezra is the son of Allah, and the Christians say: Messiah is the son of Allah. That is a saying from their mouths. They imitate the saying of disbelievers of old. Allah's Curse be on them, how they are deluded away from the truth! >> (Surah 4:171)

<< And (both) the Jews and Christians say: "We are the children of Allah and His beloved ones." Say: "Why then does He punish you of your sins?" Nay, you are but human beings, of those He has created, He forgives whom He wills and He punishes whom He wills. And to Allah belongs the dominion of heavens and the earth and all that is between them, and to Him is the return (of all) >> (Surah 5:18)

Jesus is a human being, eats and drinks and do all the humans stuff:

Jesus (peace be upon him) is only a slave and a Messenger of Allah. But Christians loved him so much that they exaggerate in praising him till they made him as a son of Allah. Narrated Umar: I heard the prophet (peace be upon him) saying, "Don't exaggerate in praising me as the Christians praised the son of Mary, for I am only a slave. So, call me the slave of Allah and His Messenger." And Almighty Allah declared:

<< The Messiah (Jesus), son of Mary, was no more than a Messenger; many were the Messengers that passed away before him. His mother (Mary) was Siddiqah [i.e. she believe in Words of Allah and His Books.] They both used to eat food (as any other human being, while Allah does not eat). Look how We make the Ayat (proofs, evidences, verses, lessons, signs, revelations, etc.) clear to them, yet look how they are deluded away (from the truth).>> (Surah 5:72)

Allah said that Jesus eats food. That means he needs others to grow food and someone to cock it. So, Jesus needs others while Allah does not need anybody but everybody needs him.

Some of the Christians had gone far beyond that. They said that the Messiah (Jesus) is Allah. Allah the Almighty said:

<< Surely, they have disbelieved who say: "Allah is the Messiah (Jesus), son of Mary." But the Messiah (Jesus) said: "O Children of Israel! Worship Allah, my Lord and your Lord." Verily, whosoever sets up partners in worship with Allah, then Allah has forbidden Paradise for him, and Fire will be his abode. And for the Zalimun (polytheists, and wrongdoers) there are no helpers. >> (Surah 5:72)

<< Surely, in disbelief are they who say that Allah is the Messiah, son of Mary. Say (O Muhammad): "Who then has the least power against Allah, if He were to destroy the Messiah, son of Mary, his mother, and all those who are on earth together?" And to Allah belongs the dominion of heavens and earth, and all that between them. He creates what He wills. And Allah is able to do all things. >> (Surah 5:17)

Also, some of the Christians said that Allah is three (the Trinity). Praise Be to Allah. Allah the Exalted said:

<< Surely, disbelievers are those who said: "Allah is the third of the three (in a Trinity)." But there is no Ilah (god) (none who has the right to be worshiped but Allah) but One Ilah (God - Allah). And if they cease not from what they say, verily, a painful torment will befall the disbelievers among them. >> (Surah 5:73)

<< And say: "All the praises and thanks be to Allah, Who has not begotten a son (nor an offspring), and Who has no partner in (His) Dominion, nor He is low to have a Wali (helper, protector or supporter). And magnify Him with all the magnificence, [Allahu-Akbar (Allh is the Most Great)]." >> (Surah 17:111)

And to all Christians and those who worship the Messiah beside Allah, Allah warns them that the Messiah will witness against them. Allah the Exalted said:

<< And (remember) when Allah will say (on the Day of Resurrection): "O Jesus son of Mary! Did you say unto men: 'Worship me and my mother as two gods besides Allah?'" He will say: "Glory be to You! It was not for me to say what I had not right (to say). Had I said such a thing, You would surely have known it. You know what is in my inner-self though I do not know what is in Yours, truly, You, only You, are the All-Knower of all that is hidden and unseen. Never did I say to them aught except what You (Allah) did command me to say: 'Worship Allah, my Lord and your Lord', And I was a witness over them while I dwelt amongest them, but when You took me up, You were the Watcher over them, and You are a Witness to all things. If you punish them, they are Your slaves, and if You forgive them, Verily You, only You are the All-Mighty, the All-Wise.">> (Surah 5: 116-120)