‘You stand, Harry Potter, upon the remains of my late father,’ he hissed softly. ‘A Muggle and a fool… very like your dear mother.’
Wasn’t Harry’s mother a witch? Her parents were Muggles. That would make her a mudblood; not a Muggle. Wouldn’t it?
Well, he said “very like”, not “exactly like”. 
It’s been established that Voldemort and crew see little difference between Muggles and Muggle-born (thus the basilisk), and hate them both.
Must be the way I read sentences. I took him to say, ‘A Muggle and a fool… very like your dear mother [was a Muggle].’
It’s like when someone says, ‘He is taller than I.’ Which means, ‘He is taller than I am tall.’
According to JK Rowling (full question and answer in the link), people like Voldemort or the Malfoys don’t care whether or not someone is technically a witch or wizard. If they have any close shred of Muggle blood in them, they’re Mudbloods.
Harry’s mother was the sister of the nasty aunt he lives with, and she is obviously a muggle from the viterpritude she refers to her sister as being a witch … go back and reread potter1
Maybe… 
During the last interview, someone asked Rowling if Petunia was a squib. Rowling answered:
So there’s something about Petunia.
As for Harry’s mother, Agrippina got it. The Purebloods consider a person a “mudblood” and even a Muggle for generations (we’re never really sure how far back you have to go to be considered “pure)”.
Look at the other side of the quote, I think Voldy is calling Lily a fool; a fool for allowing herself to be killed in trying to protect her son. Maybe a fool for other reasons as well, but mostly a fool for love, something Dumbledore has said Voldy does not (cannot?) understand.
I’ve wondered for a while if Petunia was a witch, that is to say at some time in the past she could use witchcraft – but she used it just the once to turn herself into a muggle. I got the idea from a character in Diana Wynne Jones "Witch Week"who did something similar.
dont know how to do one of the spoiler things, but in a later porrer book, petunia is family and his living with family provides protection while he is away from Hogwards. Petunia gets a screamer thingy telling her to remember the agreement to keep Harry.
sorry but i have a crashing migraine onset and am waiting for meds to kick in=( would be better but I cant think right now
Petunia is a Muggle, but Harry’s mother was a witch. If she’s a witch, then she’s not a Muggle. (Didn’t Harry’s parents meet at Hogwarts, BTW? ISTR a scene where Harry’s mom get mad at his dad for being mean to Snape.) It sounds to me that, either purposly (trying to get Harry’s goat) or accidentally, Voldemort called her a Muggle.
Lilly is Muggle-born. She was a witch in a family of Muggles.
And you can’t believe anything Old Snake Eyes says. Tom Riddle’s father was a Muggle. The whole “Pure Bloods Are The Only Way” Movement is being led by a Mudblood.
I doubt it would have to have been so complicated.
Another detail Rowling let slip was that Dumbledore had been in correspondance with Petunia before the Potters senior died – not with the Evans family, but with Petunia specifically.
Petunia is the older sister. This has lead some to speculate that Lily was the second child in the family to get the letter.
The idea is that Petunia heard about it and was scared and/or disgusted, and refused. Thus she would never have had a wand, or training, but might still have powers. And as she watched Lily, she must have realized all the opportunities she missed and became resentful.
So there you have it – all of her prejudices would come down to the internalized self-loathing of a closet witch
Yes, by a mudblood who’s father rejected his witch mother which (Voldy implies) lead to her early death and Tom Riddle being raised in a muggle orphanage. Given the long tradition of English literature of orphanages being horrible places, it’s no wonder Voldly deeply resents his father and wishes his mum had married a fellow pure-blood.
I think we can belive Voldy in this: he hates and resents any muggle or mudblood. His definition of what a muggle or a mudblood is very “generoous”.
Hadn’t thought about it before, but the Voldy’s dad is Muggle is eerily reminiscient of the old “Hitler was part Jewish” rumors. Not to Godwinize the thread or anything.
Voldemort does cast a wider net; but I thought through the series that “Mudblood” specifically meant that the wizard had a Muggle parent. I had a “Wait a tic!” moment when Voldemort called Harry a Mudblood.
ISTR Malfoy mentioning something about Harry not having to worry about being attacked by something since both of his parents were magical, but Hermione did. (Chamber of Secrets?) i.e., Harry’s not a Mudblood.
When Slytherin founded his house, he only accepted “pureblood” wizards and witches (c.f. the Sorting Hat’s song in Order of the Phoenix). The Sorting Hat nearly put Harry into Slytherin, so Harry must by Slytherin’s definition be a “pureblood” (c.f. The Philosopher’s Stone). So by Slytherin’s own definition, a magical person is a “pureblood” even if a grandparent was a muggle but both parents were magical.
“Mudblood” is a racial slur, not an anthropological term. Rowling’s characters do not use it in a precise and logical manner, and you’re missing the point if you expect them to. For most racists, having only one parent of the despised race is usually considered no better than having both. For sufficiently bigoted wizards, anyone tainted by even “one drop” of non-magical blood is probably considered a “Mudblood”.
I don’t think the Sorting Hat cares about how Slytherin would have defined “pureblood”.
Voldy himself was in Slytherin despite having one non-magical parent, so either Slytherin’s definition was much looser than that (so loose as to be meaningless), or, like I said, the Sorting Hat doesn’t care.
I think that the Sorting Hat is much simpler than following the wishes of the original Four, though they might have thought that when they enchanted it. From all that we’ve seen, it simply puts every student where that student wants to go. It might have some leeway for undecided students (this would enable it to balance the houses), and it certainly makes suggestions, but from what we’ve seen, it looks like the student always has final say. Thus, for instance, Harry chooses “anything but Slytherin”, and the hat then chooses Griffindor for him, based on him being well-suited for that house, and possibly influenced by where it was putting other students.
And I think that Lamia nailed the usage of “mudblood” as being purely a racial slur, and hence inherently illogical and inconsistent.