It only makes sense to compare "ссориться" and "спорить" because "ссорить" is a transitive verb. "Ссориться" means "to quarrel, to disagree", in general. "Спорить" is "to dispute" some specific questions trying to defend your point of view and disprove an opponent's POV.
Examples:
"Они с девушкой постоянно ссорятся"
"Мы спорили всю ночь. Так ни к чему и не пришли"

"Ссорить" is a transitive verb which means "to make some people quarrel with each other" (you need to specify these people as an object of a sentence). It is good to know... but as for a learner - this verb isn't you highest priority.