People who sincerely examined Islam and were searching for God were guided to Islam as says God in Quran:
29:69 And those who strive in Our (cause),- We will certainly guide them to our paths: For verily Allah is with those who do right.وَالَّذِينَ جَاهَدُوا فِينَا لَنَهْدِيَنَّهُمْ سُبُلَنَا وَإِنَّ اللَّهَ لَمَعَ الْمُحْسِنِينَ (29:69)
For disbelief in Islam there are lot of reasons:
1- One of the most common and sadly most stupid is envy. God has chosen someone to his message and people instead of enjoying his message they enjoyed fighting the messenger and envying him:
2:90 Evil is that for which they sell their souls: that they should disbelieve in that which Allah hath revealed, grudging that Allah should reveal of His bounty unto whom He will of His bondmen. They have incurred anger upon anger. For disbelievers is a shameful doom.بِئْسَمَا اشْتَرَوْاْ بِهِ أَنفُسَهُمْ أَن يَكْفُرُواْ بِمَا أنَزَلَ اللّهُ بَغْياً أَن يُنَزِّلُ اللّهُ مِن فَضْلِهِ عَلَى مَن يَشَاء مِنْ عِبَادِهِ فَبَآؤُواْ بِغَضَبٍ عَلَى غَضَبٍ وَلِلْكَافِرِينَ عَذَابٌ مُّهِينٌ (
2- Arrogance for love of arrogance:
7:76 [But] the arrogant ones said: "Behold, what you have come to believe in we refuse to regard as true!"قَالَ الَّذِينَ اسْتَكْبَرُواْ إِنَّا بِالَّذِيَ آمَنتُمْ بِهِ كَافِرُونَ (7:76)
3- False pride that they are better than those who follow the religion of Islam:
2:13 And when they are told, "believe as other people believe," they answer, "Shall we believe as the weak-minded believe?" Oh, verily, it is they, they who are weak-minded -but they know it not!وَإِذَا قِيلَ لَهُمْ آمِنُواْ كَمَا آمَنَ النَّاسُ قَالُواْ أَنُؤْمِنُ كَمَا آمَنَ السُّفَهَاء أَلا إِنَّهُمْ هُمُ السُّفَهَاء وَلَـكِن لاَّ يَعْلَمُونَ (2:13)
4- Enjoying wickedness, some of the disbelievers enjoyed expressing their faith in Islam and meantime they were the worst enemies to Islam. Muhammad (PBUH) had to bear with them.
2:14 And when they meet those who have attained to faith, they assert, "We believe [as you believe]"; but when they find themselves alone with their- evil impulses,they say, "Verily, we are with you; we were only mocking!"وَإِذَا لَقُواْ الَّذِينَ آمَنُواْ قَالُواْ آمَنَّا وَإِذَا خَلَوْاْ إِلَى شَيَاطِينِهِمْ قَالُواْ إِنَّا مَعَكْمْ إِنَّمَا نَحْنُ مُسْتَهْزِؤُونَ (2:14)
5- God did not let them believe, because they were not sincere to believe.
6:25 And there are among them such as [seem to] listen to thee [O Prophet]: but over their hearts We have laid veils which prevent them from grasping the truth, and into their ears, deafness. And were they to see every sign [of the truth], they would still not believe in it-so much so that when they come unto thee to contend with thee, those who are bent on denying the truth say, "This is nothing but fables of ancient times!"وَمِنْهُم مَّن يَسْتَمِعُ إِلَيْكَ وَجَعَلْنَا عَلَى قُلُوبِهِمْ أَكِنَّةً أَن يَفْقَهُوهُ وَفِي آذَانِهِمْ وَقْرًا وَإِن يَرَوْاْ كُلَّ آيَةٍ لاَّ يُؤْمِنُواْ بِهَا حَتَّى إِذَا جَآؤُوكَ يُجَادِلُونَكَ يَقُولُ الَّذِينَ كَفَرُواْ إِنْ هَذَآ إِلاَّ أَسَاطِيرُ الأَوَّلِينَ (6:25)
6- Some people of the book at the time of the prophet they knew him as was described to them in their holy book but they chose to disobey God. Many just would not accept a prophet not from them. Though it was God not Muhammad (PBUH) who decided who to carry the message.
6:20 Those unto whom We gave the Scripture recognize (this Revelation) as they recognize their sons. Those who ruin their own souls will not believe.الَّذِينَ آتَيْنَاهُمُ الْكِتَابَ يَعْرِفُونَهُ كَمَا يَعْرِفُونَ أَبْنَاءهُمُ الَّذِينَ خَسِرُواْ أَنفُسَهُمْ فَهُمْ لاَ يُؤْمِنُونَ (6:20)
In the contrary some of the people of the book believed in him and followed Islam. It happened particularly more after his death.
3:199 And, behold, among the followers of earlier revelation there are indeed such as [truly] believe in God, and in that which has been bestowed from on high upon you as well as in that which has been bestowed upon them. Standing in awe of God, they do not barter away God's messages for a trifling gain. They shall have their reward with their Sustainer - for, behold, God is swift in reckoning!وَإِنَّ مِنْ أَهْلِ الْكِتَابِ لَمَن يُؤْمِنُ بِاللّهِ وَمَا أُنزِلَ إِلَيْكُمْ وَمَآ أُنزِلَ إِلَيْهِمْ خَاشِعِينَ لِلّهِ لاَ يَشْتَرُونَ بِآيَاتِ اللّهِ ثَمَنًا قَلِيلاً أُوْلَـئِكَ لَهُمْ أَجْرُهُمْ عِندَ رَبِّهِمْ إِنَّ اللّهَ سَرِيعُ الْحِسَابِ
7- "I will not believe until I see God, period." this happened with some of disbelievers at time of Muhammad as with the Jews that were at time of prophet Moses.
2:55 And [remember] when you said, "O Moses. indeed we shall not believe thee unto we see God face to face!" - whereupon the thunderbolt of punishment overtook you before your very eyes.وَإِذْ قُلْتُمْ يَا مُوسَى لَن نُّؤْمِنَ لَكَ حَتَّى نَرَى اللَّهَ جَهْرَةً فَأَخَذَتْكُمُ الصَّاعِقَةُ وَأَنتُمْ تَنظُرُونَ (2:55)
We have the right to have evidences of God existence to believe which are many and God has the right to decide when he will let us see him. His great pleasure when we recognize him mentally and spiritually. If we fail to do that we may not even recognize him when we see him or when he send his angles or other strong proofs.
6:111 And even if We were to send down angels unto them, and if the dead were to speak unto them and [even if] We were to assemble before them, face to face, all the things [that can prove the truth], they would still not believe unless God so willed But [of this] most of them are entirely unaware.وَلَوْ أَنَّنَا نَزَّلْنَا إِلَيْهِمُ الْمَلآئِكَةَ وَكَلَّمَهُمُ الْمَوْتَى وَحَشَرْنَا عَلَيْهِمْ كُلَّ شَيْءٍ قُبُلاً مَّا كَانُواْ لِيُؤْمِنُواْ إِلاَّ أَن يَشَاء اللّهُ وَلَـكِنَّ أَكْثَرَهُمْ يَجْهَلُونَ (6:111)
The will of God is important in our guidance and it depends in our sincerity to find him.
6:125 And whomsoever God wills to guide, his bosom He opens wide with willingness towards self-surrender [unto Him]; and whomsoever He wills to let go astray, his bosom He causes to be tight and constricted, as if he were climbing unto the skies: it is thus that God inflicts horror upon those who will not believe.فَمَن يُرِدِ اللّهُ أَن يَهْدِيَهُ يَشْرَحْ صَدْرَهُ لِلإِسْلاَمِ وَمَن يُرِدْ أَن يُضِلَّهُ يَجْعَلْ صَدْرَهُ ضَيِّقًا حَرَجًا
كَأَنَّمَا يَصَّعَّدُ فِي السَّمَاء كَذَلِكَ يَجْعَلُ اللّهُ الرِّجْسَ عَلَى الَّذِينَ لاَ يُؤْمِنُونَ
Many in the west who disbelieve in Islam do that out of lack of good information or misinformation about Islam. For Christians particularly the main doctrines of their religion divinity of Jesus, Trinity and salvation are in odd with Islam. The reference books to all of us are the three Revelations: old testament, Gospels and Quran. That is why dialogue between Christians and Muslims religious leaders would help all of us to reach the truth.