The use of violence is against Islam and it is not allowable, except in cases of self-defense or deserved punishment. The Holy Qur'an says:

1. "And fight in the way of Allah those who fight you, but transgress not the limits. Truly, Allah likes not the transgressors."
2. "And kill them wherever you find them, and turn them out from where they have turned you out."
3. "But if they cease, let there be no transgression except against the polytheists, and wrong-doers."
4. "And if you punish then punish them with the like of that with which you were afflicted. But if you endure patiently, verily it is better for the patient."

As you see Allah is desiring to forgive. Not only but in some Verse God asked Muslims to deal kindly with non Muslims as in: "Forbidden not Allah unto you regarding those who have not made war upon you in the matter of (your) religion, and drove you out of your homes, that ye show them kindness and deal justly with them; Allah loves those who deal with equity".

Suicide bombers believe only, or have been taught only, the parts of the verses in BOLD. And when they kill they make no distinction between Muslims and non-Muslims, believers or non-believers, Battlefields or Cities, Worriers or Women, Children and Old Men( because Islam did forbid the killing of women, Children and old Men even in the battlefields) They believe that only they are right and everybody else who disagrees with them must be killed. Such ideas were popular during the time of Imam Ali and he was killed by one of them.

Sadly. whatever I say here will be useless and will not effect them because they believe that they are scholars and know everything about the religion. But, in fact, they live in darkness with lack of knowledge and they are enemies of humanity.