In most universities professors are encouraged to be transparent about grading, but whether they have to show you your grades is up to university/department policy.
If it’s important to you then seek recourse elsewhere: does your school have an ombudsperson or undergraduate academic support? If so - ask them to help mediate. It may also be helpful if you get other students on board: if you’re the only one complaining it’s less likely that you’ll be taken seriously.
In my department, for example, I have to tell students exactly how much they got in each assessment criterion (assignment/project/exam etc.). In addition, I must tell them (in the syllabus, before the course starts) what the numerical to letter grade conversions are (so what grade qualifies you for an A+/A/A- etc.). But this is by no means the norm in other universities to my knowledge.