Christianity and Islam are one of the Sibling Religions which are JUDAISM, CHRISTIANITY AND ISLAM. The sibling Religions were thus referred to based on the fact that they all originated from one source which is Father Abraham. Abraham had two Sons which was Ishmael and Isaac. Ishmael was given birth by Hagar, the maid of Sarah, who she gave to Abraham as wife, because she, Sarah was barren. But later on, Sarah also gave birth to Isaac.
When Hagar gave birth to Ishmael, she saw herself as the one who had given birth to Abraham and as such her attitude changed. She did not accord her mistress Sarah the needed respect.
By virtue of the fact that Hagar’s attitude changed after giving birth to Abraham, Sarah saw that if Abraham were to leave to the land of the dead, Hagar would see herself as equal with Sarah and even claim inheritance for her son Ishmael who was actually the elder. To avoid future inheritance dispute which could deny her son Isaac as the heir to Abraham’s inheritance, Sarah asked Hagar to leave the house of Abraham since she was no more her slave. When Sarah told Abraham, he was not pleased with that suggestion by Sarah, but the God of Abraham, who knows the future, asked Abraham to comply to the request by Sarah. Abraham thus had no option than to send Hagar and her son Ishmael away with some goods and some servants.
After the departure of Hagar, Sarah continued her duty as wife to Abraham till her death. Through her son Isaac who gave birth to Jacob, the nation of Israel was established. Through Moses, YHWH, the God of Israel established the religion of Judaism. Jesus who was YHWH the God of Israel came later came down to live with them and also practiced the religion of Judaism, but he was rejected and crucified, as had been earlier on been prophesied. After the death and resurrection of Jesus, the twelve disciples and the Apostles established Christianity.
Several years later, God had to send a descendant of Ishmael, by name of Muhammed or Mohammed (PBUH) to establish the Religion of Islam.
As the religion of Christianity and Islam both originated from the descendants of Abraham, Christianity and Islam are thus brothers and part of the Sibling Religion which are Judaism, Christianity and Islam.