Hermione was about to run off into the magical world, possibly never to return.

So I can see her wanting to remove their knowledge of her, and the magical world, from her parents’ memories for several reasons :-

a) To prevent her parents coming to look for her. If she is going to be gone for an entire year and they don’t know where she is, there might be a temptation for them to come after her.

b) To prevent the Death Eaters torturing the information out of her parents. If her parents have some of where she might be going (The Burrow, Hogwarts, Godric’s Hollow etc) then the Death Eaters might find that information with torture or legilimency. And while the Death Eaters might torture her parents anyway, at least that information would remain safe.

c) To prevent the secret of the magical world leaking out. If her parents were REALLY worried they might go to the police or the secret service (of some type) if their daughter didn’t return. Which would open up a whole can of worms that might never be closed again. However if they don’t realise that their daughter is gone then they won’t know she is missing.

d) To spare them the pain and suffering of losing a child. No parent should outlive their child. It is a horrific ordeal that no one should ever suffer through. Hermione knows she is going to war - a war she, in all likelihood, is not going to come back from. But she knows she has no choice - she can’t abandon Harry and she can’t abandon the magical world. So rather than let her parents talk her out of it, and rather than let them face the possibility of her dying in that war, she gives them the most merciful option - to forget they ever had a child.

I think that - of all the brave things Hermione does throughout the books - this is on a par to standing up to Bellatrix in Malfoy Manor.