It's called empathy. Look it up. It's very different from sympathy, which is what I think you are referring to.
You can understand a rapist without accepting his motives and without having sympathy for his actions.
Empathy is to put yourself in once shoes and understand them from where they are coming/standing.
The two parisian murders grew up without their parents (both died young) in a shithole of a suburb and with crime around them and a bleak future. They were clearly lost and looking for identity and the feeling of 'belonging' (look it up it's an interesting psychology theory) somewhere which led them to radical Islam. They could have been gangsters, hooligans or free masons as well.
See now I've tried to understand the attackers without showing sympathy for their actions since I find them horrible, but from my understanding of them I might find a reason and therefore [maybe] a solution to prevent soem from turning to the extreme version of Islam.
One you scream out loud: ISLAM ISLAM ISLAM is the reason. You are doing nothing but yelling.
Empathy? Not, it's called critical thinking vs. religion
Bible
Anyone arrogant enough to reject the verdict of the judge or of the priest who represents the LORD your God must be put to death. Such evil must be purged from Israel. (Deuteronomy 17:12 NLT)
You should not let a sorceress live. (Exodus 22:17 NAB)
If a man lies with a male as with a women, both of them shall be put to death for their abominable deed; they have forfeited their lives. (Leviticus 20:13 NAB)
A man or a woman who acts as a medium or fortuneteller shall be put to death by stoning; they have no one but themselves to blame for their death. (Leviticus 20:27 NAB)
If a man is caught in the act of raping a young woman who is not engaged, he must pay fifty pieces of silver to her father. Then he must marry the young woman because he violated her, and he will never be allowed to divorce her. (Deuteronomy 22:28-29 NLT)
Quran
Bukhari (52:177) - Allah's Apostle said, "The Hour will not be established until you fight with the Jews, and the stone behind which a Jew will be hiding will say. "O Muslim! There is a Jew hiding behind me, so kill him."
Bukhari (52:256) - The Prophet... was asked whether it was permissible to attack the pagan warriors at night with the probability of exposing their women and children to danger. The Prophet replied, "They (i.e. women and children) are from them (i.e. pagans)."
Bukhari (52:220) - Allah's Apostle said... 'I have been made victorious with terror'
Abu Dawud (14:2526) - The Prophet (peace_be_upon_him) said: Three things are the roots of faith: to refrain from (killing) a person who utters, "There is no god but Allah" and not to declare him unbeliever whatever sin he commits, and not to excommunicate him from Islam for his any action; and jihad will be performed continuously since the day Allah sent me as a prophet until the day the last member of my community will fight with the Dajjal (Antichrist)
HOW CAN SOMEONE BE IN SYMPATHY with this shit? HOW?