His parents, David and Elizabeth Goniwe, were farm labourers and lived in the Emaqgubeni section of the old Cradock, Eastern Cape township.
He obtained a teachers' diploma from University of Fort Hare and returned to Sam Xhallie School to teach mathematics and science.
[1] Goniwe went to further his studies at Fort Hare University where he obtained a teacher’s diploma, majoring in mathematics, education, physics, and chemistry.
In 1972, he left his job to pursue a Bachelor of Science Degree at Fort Hare but was told that spaces were reserved for students straight from high school.
[1] Goniwe’s political views were influenced by Reverend Canon James Calata, a founding member and former secretary of the South African Native National Congress.
Goniwe established a Marxist cell which was a reading group which studied Marxism and Communism, together with Dumisa and Lungisile Ntsebeza, Meluxolo Silinga and Michael Mgodolozi.
In 1975, Dumisa, Ntsebeza, Silinga, and Mgodolozi were arrested after one member of the group gave the police information about their underground work.
[1] While in jail, he studied and obtained a Bachelor of Arts Degree through the University of South Africa, majoring in political science and education.
That same year, the Cradock Youth Association (CRADOYA) was launched and Goniwe became its first Chairperson and Fort Calata, a friend and colleague, became the secretary.
Louis le Grange was Minister of Law and Order at the time and banned all meetings for three months, leading to further riots breaking out.
On 26 June 1985, CRADORA celebrated 30 years of the Freedom Charter where Goniwe delivered the keynote address on its formation in Kliptown.
[3][11][2] A funeral was held for Goniwe, Calata, Mkhonto and Mhlauli on 20 July 1985 where Allan Boesak, Beyers Naudé and Steve Tshwete gave keynote addresses.
[1] The South African Democratic Teachers Union, the largest teacher union in the Southern Hemisphere, has also named its head office as "Matthew Goniwe House" as a revolutionary symbol in memory of the role he played in the struggle of shaping South African society, education in particular.