“I cannot follow a religion that keeps producing terrorists and calls itself merciful.”
The objection has weight, and it should not be waved away with a slogan.
Start with what the text says. Qur'an 5:32 states that whoever kills one innocent soul has killed all humanity, and whoever saves one soul has saved all humanity. The Prophet explicitly forbade the killing of non-combatants, women, and children. Muslim organisations across the world condemned the attacks in New York and in London as violations of Islam's own fundamental principles.
Now the harder half. Men have committed atrocities while shouting the name of this religion, and pointing to a verse does not make their victims less dead. Anyone who answers this doubt by quoting 5:32 and then falling silent has answered nothing.
The verses that get cited to justify indiscriminate killing are verses about war, addressed to particular circumstances, hedged by conditions. Islamic law permits the use of force under a legitimate authority, in defence against persecution, oppression, and the seizure of land. It does not authorise a man with a bomb to appoint himself an army. The extremist and the polemicist arrive at the same reading of these verses, and they need each other to sustain it.
Every tradition with a billion adherents contains people who disgrace it. The question is whether the disgrace follows from the teaching or violates it, and that question is answerable by reading the teaching.
The reader who is repelled by violence carried out in Islam's name is responding to something real. That instinct is not evidence against the faith. It is the instinct the faith asks for.