I have two categorical (binary) variables: Gender (female vs. male) and 3 subject exams (English, Math, Science: Pass or fail). Everyone took all the subject exams (repeated measures). How can I analyze this kind of data to see the gender difference (e.g., Are female students more likely to pass English exams than males AND are female students more likely to pass English than Math?) when my exam variable is repeated measure/dependent in SPSS? Can I use mcnemar's test?
If you take the tests one at a time, then the Gender by outcome (pass/fail) table for each one is a 2x2 table of independent counts that can be analyzed with a simple chi-square test or a binary logistic regression.
If you want to also formally test whether any Gender differences in outcomes differ across subject areas, then you'd have a 2x3 design, with Gender as a between-subjects factor and subject matter or test type as a within-subjects or repeated-measures factor. In SPSS this kind of design can be analyzed using generalized estimating equations (GEE) in the GENLIN proceedure (Analyze>Generalized Linear Model>Generalized Estimating Equations), or as a generalized linear mixed model (GLMM) in the GENLINMIXED procedure (Analyze>Mixed Models>Generalized Linear). Both procedures offer binary logistic models as options. GENLIN with GEE is a bit easier to use.
In either case, the data need to be set up with three cases per subject, including a subject ID variable, a Gender variable, a test type variable, and a binary outcome variable.
There is an example Case Study at https://www.ibm.com/support/knowledgecenter/en/SSLVMB_27.0.0/statistics_casestudies_project_ddita/spss/tutorials/gee_wheeze_intro.html that walks you through a repeated-measures binary logistic model in GENLIN. The structure (one between-subjects factor and one repeated-measures factor) is identical to yours, though of course the variables are different (and the repeated factor has four levels rather than three, but no different concepts are involved).