1) Islam was not spread by the sword. While war is permitted in self-defense and to establish justice, the Quran makes clear that initiating hostilities or aggression is forbidden.
2) Islam spread rapidly during periods of peace, not war. Many historians have rejected the myth that early Muslims forced conversion at sword-point. Islam appealed to people through its rational and simple teachings as well as impressive rituals.
3) When Muslim armies entered places like Makkah and Jerusalem, there was no bloodshed or forced conversion - people were free to stay or leave as they chose. This contrasts with violence during the Crusades. Indonesia and East Africa also entered Islam peacefully, without military conquest.