Short answer: Islam encourages Muslims to fight unbelievers until they are converted to Islam.
The Scripture of Muslims (Qur’an):
Quran 9:29—Fight those who do not believe in Allah or in the Last Day and who do not consider unlawful what Allah and His Messenger have made unlawful and who do not adopt the religion of truth from those who were given the Scripture – [fight] until they give the jizyah willingly while they are humbled.
Quran 8:38-39–Say to those who have disbelieved [that] if they cease, what has previously occurred will be forgiven for them. But if they return [to hostility] – then the precedent of the former [rebellious] peoples has already taken place.And fight them until there is no fitnah and [until] the religion, all of it, is for Allah . And if they cease – then indeed, Allah is Seeing of what they do.
Quran 9:5–And when the sacred months have passed, then kill the polytheists wherever you find them and capture them and besiege them and sit in wait for them at every place of ambush. But if they should repent, establish prayer, and give zakah, let them [go] on their way. Indeed, Allah is Forgiving and Merciful.
Quran 2:193—Fight them until there is no [more] fitnah and [until] worship is [acknowledged to be] for Allah . But if they cease, then there is to be no aggression except against the oppressors.
The Traditions of Muhammad (Hadith):
Sahih al-Bukhari 25–Narrated Ibn ‘Umar: Allah’s Messenger (ﷺ) said: “I have been ordered (by Allah) to fight against the people until they testify that none has the right to be worshipped but Allah and that Muhammad is Allah’s Messenger (ﷺ), and offer the prayers perfectly and give the obligatory charity, so if they perform that, then they save their lives and property from me except for Islamic laws and then their reckoning (accounts) will be done by Allah.”
Sahih Muslim 1731— Muhammad ordered: Fight in the name of Allah and in the way of Allah. Fight against those who disbelieve in Allah. Make a holy war…When you meet your enemies who are polytheists, invite them to three courses of action. If they respond to any one of these, you also accept it and withhold yourself from doing them any harm. Invite them to (accept) Islam; if they respond to you, accept it from them and desist from fighting against them. Then invite them to migrate from their lands to the land of the Muhajireen and inform them that, if they do so, they shall have all the privileges and obligations of the Muhajireen. If they refuse to migrate, tell them that they will have the status of Bedouin Muslims and will be subjected to the Commands of Allah like other Muslims, but they will not get any share from the spoils of war or Fai’ except when they actually fight with the Muslims (against the disbelievers). If they refuse to accept Islam, demand from them the Jizya. If they agree to pay, accept it from them and hold off your hands. If they refuse to pay the tax, seek Allah’s help and fight them.
Sahih al-Bukhari 392–Narrated Anas bin Malik: Allah’s Messenger (ﷺ) said, “I have been ordered to fight the people till they say: ‘None has the right to be worshipped but Allah.’ And if they say so, pray like our prayers, face our Qibla and slaughter as we slaughter, then their blood and property will be sacred to us and we will not interfere with them except legally and their reckoning will be with Allah.”
Sahih al-Bukhari 3167–Narrated Abu Huraira: While we were in the Mosque, the Prophet (ﷺ) came out and said, “Let us go to the Jews” We went out till we reached Bait-ul-Midras. He said to them, “If you embrace Islam, you will be safe. You should know that the earth belongs to Allah and His Apostle, and I want to expel you from this land. So, if anyone amongst you owns some property, he is permitted to sell it, otherwise you should know that the Earth belongs to Allah and His Apostle.”
Sahih al-Bukhari 4557–Narrated Abu Huraira: The Verse:–“You (true Muslims) are the best of peoples ever raised up for mankind.” means, the best of peoples for the people, as you bring them with chains on their necks till they embrace Islam.
Sahih al-Bukhari 4357–Narrated Qais: One day while he was using them (i.e. arrows of divination), Jarir stopped there and said to him, “Break them (i.e. the arrows) and testify that None has the right to be worshipped except Allah, or else I will chop off your neck.” So the man broke those arrows and testified that none has the right to be worshipped except Allah… So when the messenger reached the Prophet, he said, “O Allah’s Messenger (ﷺ)! By Him Who sent you with the Truth, I did not leave it till it was like a scabby camel.” Then the Prophet (ﷺ) blessed the horses of Ahmas and their men five times.
Sahih Muslim 2405–Allah’s Messenger (ﷺ) called ‘Ali b. Abu Talib and he conferred (this honour) upon him and said: Proceed on and do not look about until Allah grants you victory, and ‘Ali went a bit and then halted and did not look about and then said in a loud voice: Allah’s Messenger, on what issue should I fight with the people? Thereupon he (the Prophet) said: Fight with them until they bear testimony to the fact that there is no god but Allah and Muhammad is his Messenger
This short overview of the Quran and hadith demonstrates that Islam permits forced conversions. Muhammad’s companion, Ali asks Muhammad, ‘on what issue should I fight with the people?’ Muhammad responds, ‘Fight with them until they bear testimony to the fact that there is no god but Allah and Muhammad is his Messenger.’
The reason why forced conversion exists in Islamic countries is the teaching of Islam. In our political correctness, we can usually blame it on other things, such as poverty, lack of education, etc. But the truth is that Islam sanctions forced conversions.