Feryal Matar was born in 1942 in the Palestinian village of al-Majdal. In 1948, Matar and her family were forcefully displaced from their home by armed Zionist militias and settled in al-Shati refugee camp in the Egyptian-administered Gaza Strip. Her father was martyred during the struggle. Matar took an interest in art from a young age and, by 15, was employed by UNRWA as an art teacher, working with children in the refugee camp. Matar graduated from the Girls' Gazzah College with a secondary education certificate issued by the Egyptian Department of Education in Cairo. Matar continued to teach art in the Gaza Strip until her move to Kuwait in 1965, where she taught, practiced, and exhibited her work. She met her husband, the family doctor and fellow Palestinian refugee Zuhair AbuKuwaik, in Kuwait, and the couple married in 1967. That same year, they moved to Sharjah in the United Arab Emirates, where Matar began teaching art at the Asmaa Girls' School as part of the Kuwaiti Educational Assistance Program, with her contract being issued by the Kuwait State Office in Dubai. Upon arriving in Sharjah, Matar and her husband bought a piece of land in an area now known as the Heart of Sharjah, where Matar planted and cultivated seeds from Palestine. The property hosted dignitaries and businessmen passing through the region, and housed Matar's art studio. The site is also where Matar's husband, a family physician, established the first medical clinic in Sharjah. Matar began engaging her students in exhibitions and public displays early on, including one in 1969. Sheikha Noura [Al-Qassimi] opened the exhibition at Asmaa Girls' School, featuring a selection of paintings and mixed-media works by Matar depicting themes of Palestinian heritage and liberation, and providing young students with an opportunity to engage with art and exhibition spaces firsthand. Matar was awarded Best Teacher in the Art Education Competition for Trucial Schools in 1972 and 1973. In the same academic year, Matar received the first Excellence Award at the Art Education Exhibition, administered by the UAE Ministry of Education. In 1974, Matar was awarded her certification in Painting and Decorating by Bennet College, based in the UK, after a year of participating in remote classes.

Matar taught art at the Sharjah Women's Union Association from its formalization under the new Federation in the mid-1970s and served as supervisor of the art committee for its annual art exhibitions. Women's Associations in the UAE, sponsored and directed by members of the Royal Family, were established across the emirates in order to encourage women to play more active roles in the young federation's social and economic development. The associations organized classes to teach a variety of skills, including literacy, and also offered women-only spaces outside the house for women to gather. The Sharjah Women's Union Association was officially registered in 1972 and joined the General Women's Union created by Sheikha Fatima Bint Mubarak in 1975. Matar's curriculum covered a variety of media, including painting, drawing, mixed-media artworks, including from found material, making flowers with media such as fabric, paper, metal, plastic, and clay; flower arrangements and painting flowers on vases and canvas; decoupage; painting on glass; metalwork; painting on textiles; painting, stencil, and wax-blocking design on silk; and interior design. In 1978, the Sharjah Women's Union Association opened its annual exhibition with 550 works in 6 sections, showcasing a variety of works from abstract paintings to traditional handicrafts, with sales totaling 30k dirhams. The exhibition also held men's-only days to encourage their engagement with women's work, signifying the role the association played in legitimizing women's social contributions. By 1981, Sheikha Noura Al-Qassimi had begun advocating to the Minister of Education for Matar to teach at the Association for more than two days a week to accommodate the high demand for her classes. Matar continued in her full-time role as an art teacher at Al-Shaima School and later at Sharjah Girls' Preparatory School, before being released from her duties as a school teacher and receiving permission to dedicate her time, as needed, to the Sharjah Women's Union Association. Matar participated yearly as a teacher in the Children's Cultural Festival as well as the Child's Art Exhibition beginning with their first annual events in 1985. By the early 90s, the Sharjah Women's Union Association had graduated women from Matar's art classes with certificates attested by the Ministry of Labor and Social Affairs, allowing them to work in business or as teachers in private schools. The art course lasted six months and enrolled women from different backgrounds, including housewives, college students, and working professionals. The women participating in the association's classes and exhibitions were able to profit from their work and expressed newfound confidence in undertaking independent endeavors, including holding exhibitions in their own homes, starting their own businesses, and permanently displaying their work for sale at the association. For those who didn't profit financially from their art, the women expressed marked improvements in their home lives through a new sense of agency gained by applying what they learned to their homes' interior decoration, and in the sense of fulfillment their children experienced from learning from their mothers. The Sharjah Women's Union Association published the monthly journal, Sawt Al-Mar'aa, which covered the association's work as well as published articles and advice columns aimed at women's issues. The association's news was often covered in the Women and Society section of Al-Ittihad Newspaper. Matar continued to exhibit her work, teach, and direct the art program at the association until her retirement.