This article explains why we don't give partial credit for SATA (select-all-that-apply) questions on quizzes.
It defeats the purpose of being able to select all that apply and only those that apply, which is the point of this question type.
Most standardized tests do not offer partial credit on multi-select questions. We do not want to give students the impression that they will receive partial credit when they encounter such questions on standardized tests.
These questions are meant to be challenging. Struggle is good for memory, and it's okay to get some questions wrong. SATA questions require students to slow down and think critically.
Students may try to "beat the system." Students who do not know the answer could select all of the answers to get some credit, as opposed to answering incorrectly and receiving no credit. Therefore, it would make more sense for a student who isn't certain of their answer to simply select everything instead of trying to puzzle out the answer. They know the answers are in there somewhere, and selecting all of them ensures some credit that they may not have otherwise received.
Teachers may offer their partial credit in different ways. If the question has 2 correct responses and the student selects all 4, should that be 50%? What if there is only 1 correct answer and all 4 are selected; is that a 50% as well, or only 25%? Allowing partial credit to be awarded would invite students to argue about their scores, which results in more headaches for you.