First - condolences for your loss, and I agree with the consensus, your supervisor was acting unprofessional.
In a real world environment, you would have an employee handbook that defined the correct protocol for any situation where you do not wish to, or cannot, come in to work. The reason for the situation determines the method in which notification occurs, and the degree to which you are "asking" or "telling".
For example, if you want a day off for a vacation, you would ask for that, and there would be a particular way in which you do that (perhaps a form, perhaps online, perhaps an email or whatnot).
If you're sick, then you would tell them that. Depending on the kind of job, there might be a designated number of sick days you're allowed to take without penalty, or no restriction (other than getting your work done), or some penalty for the first day (common in retail). There would be a designated way to tell them (most often a phone call, but you might also have an online form or something).
For deaths in the family, those are typically covered under their own rule separate from the above. Many workplaces offer a specified number of days off specifically for this case, called bereavement days. Those days typically vary based on how close of a relation (1 day for a cousin/aunt/uncle, 3 days for grandparent, 5 days for parent or sibling or spouse, for example) and are intended both to let you have some time to figure things out as well as to attend the funeral.
Bereavement days would also have a particular way in which you apply for them. I would typically consider this a tell rather than an ask, though I would probably use softer language than a sick day ("Hi boss, my grandmother passed away, so I'm going to need to take Friday off to attend the funeral.") You'd probably need to fill out a form and possibly include the death notice or similar, depending on how bureaucratic your company is (many will believe you, at least the first time).
You'd also typically want to let your boss know as soon as you can, both of the death and of the date of the funeral; since those things often are separated by several days, if you let him or her know day one of the passing, then it won't be as much of a surprise when you let them know about the funeral.
But all of that aside, in any reasonable workplace nobody would fault you for being more abrupt than usual or not following protocol exactly in this kind of situation, and any supervisor who did wouldn't be one I'd want to work for.