Islam does not encourage cousin-marriages, it simply allows it.
Islam is not the only religion which allows cousin marriage and Muslims are not the only people who practice it.
South Indian Hindus also allow and practice cousin marriage, it’s just the north Indians who consider it wrong even though Krishna’s sister married her cousin with Krishna’s approval.
Islam
The Prophet of God (peace & blessings of God be upon him) married his cousin Zaynab (may God be pleased with her).
Hinduism
Arjuna married his first cousin Subhadra the daughter of his maternal uncle Vasudeva and sister of Sri Krishna who approved of this relation.
Judaism/Christianity
Zelophehad’s daughters did as the LORD commanded Moses. Zelophehad’s daughters, Mahlah, Tirzah, Hoglah, Milcah and Noah, married their cousins on their father’s side. (Numbers 36: 1-11)
Milcah, one of Zelophehad’s daughters, was married to her cousin Nahor. They had a grand daughter named Rebekkah. In Genesis 24:48-51, the story unfolds of how, against all odds, God’s direction for her to marry her cousin’s son Isaac (first cousin once removed) is made crystal clear.
Isaac and Rebekkah had two son’s. Jacob was the son whom was blessed to fulfill God’s prophecy that the descendant’s of Abraham (Jacob’s grandfather, Isaac’s father) would become a great nation. Isaac instructed Jacob to marry a daughter of Rebekkah’s brother. Although he immediately fell in love and became engaged to his cousin Rachel, his uncle tricked him into first marrying Rachel’s sister Leah. Although God blessed Jacob greatly, Jacob suffered much grief and heartache for having married both sisters. Jacob’s descendants became what is now known as the twelve tribes of Israel. (Genesis chapters 19 and 29)
In I Chronicles 23:22, Eleazar’s daughters married their first cousins. Very little detail is given of this event.