How can I deal with being pressured by my department to pass students who failed?
Your department defers to you as the final authority on the student’s grade, and for a good reason: because you are the only person who sees the full picture of the student’s performance and the context in which it was assessed.
The department can give you high-level guidance and advice, but that is never a substitute for an instructor’s reasoned judgment taking into account the details of the situation.
The student, like all students everywhere, wants to pass, and like many (but not all) students will offer any excuse they can think of, no matter how feeble, for why they deserve lenient treatment. If the excuse rings hollow, ignore it.
Whatever your conscience dictates doing is the best course of action here. Making that final call is precisely what the department pays you to do and expects of you.