Definition of Kafir
I am almost convinced by your definition of Kaafir. However while once reading a prayer of Abu Jaahil before Ghazva Badar when he prayed from Allah to destroy those were not on straight path. And after his death it is quoted from the Prophet (AS) that his prayer was accepted. Well! But doesn’t it mean he was on the opinion of being on right path. Normally you refer to the Ayah of Quran where it is said that they recognise Prophet as they recognise their sons. Is there no possibility that that Ayah is for some particular group (May be only Jewish) not for all the persons of that time? Moreover; surah Asr says about all human being are in loss except those mentioned there (Ahl-e-Emaan). Please clarify.
A die hard Kafir of the category of Abu Jehal go through various stages: he recognized the sincerity of the prophet and yet hated him because of his excessive love for his traditions. Read Quran 21:62-68 and 27:14 for clarification of the fact that all Kafirs know that are wrong. However, to know that you are wrong is one thing and to carry a persistent feeling of guilt is quite another. It seems that many Kafirs get the opportunity to know that they were wrong, but then lose that realization because of their obsession with tradition, or arrogance, excessive indulgence in their vain desires.
Surah Asr shows that those who believe, do good deeds, and exhort each other to follow the right track are guaranteed salvation. Kafirs on the contrary are guaranteed doom in the hereafter. There are others who belong to a category between these two who may get salvation but there isn’t any guarantee for them. In other words, the people who don’t satisfy the conditions mentioned in Surah Asr would be Kafir as well as some others.
I hope I have answered the question.
In the context of above discussion, please explain Ayah 32 of Surah Infaal.
The verse tells us the following prayer (dua) of the disbelievers, (especially, Abu Jahal) “God, if this (message) is from you then send on us stones from the heavens or send us a severe punishment.” There are many other statements of the disbelievers in Quran which suggest that they were very confident that no punishment would be inflicted on them and that what they were being told was not correct. However, that doesn’t mean that deep inside they didn’t know what they were saying was wrong.
What the kuffar did at the times of prophets is similar to what a typical incorrigible criminal does: He commits a crime and then insists that he didn’t do it; in fact in many cases, criminals go on to insist that what they had done was correct. Imagine a person who forcibly usurps the property of orphans and then goes on to prove to the court of law that the property in fact belonged to him. On the one hand he is insisting that his claim is correct, while on the other he knows that he is on the wrong. That is why such people, including the kuffar, are such big criminals in the eyes of God: They not only commit crimes, they insist that their crimes are in fact not crimes; in fact those who are on the right path are criminals.
The above response to your question further clarifies who the kuffar were.