My math students consider me a harsh grader. Is my teaching attitude wrong?

Yes, you do seem to have a bad attitude toward it, but I suspect you knew that. I would suggest trying as hard as you can to put yourself in their shoes:

1. Not everyone enjoys the same things you do. What's a subject you had to take in school but didn't enjoy? Can you imagine not putting as much effort or showing as much respect to it as someone going to grad school for it?
2. It's totally rational for someone to try to maximize their grades. I think everyone finds it annoying when students push for every last point they can, especially when you don't feel they've earned it. I like to remind myself that it makes perfect sense to try to get the best grade you can for the least amount of effort. That doesn't mean you give in to their exhortations, of course, but if you understand where they're coming from then that's not incompatible with both helping them and keeping your sanity.
3. Everyone is busy. A lot of undergrads are adjusting to life away from home for the first time, are taking on responsibilities for the first time, and are probably swimming in social and extracurricular activities. That's what they're supposed to do; just keep in mind your class isn't the only thing on their plate.
4. The things you find easy, others find hard. You specifically gave some logarithmic rules as an example. To you, that's trivial. You can't understand how it's not trivial to someone else - I mean, you probably even just told them it was trivial! But I bet you can think of a field where you struggle with things an expert finds trivial. Foreign languages are a good example for me - I can hear how to say something in a new language repeatedly, and it just goes right out of my head a minute later.

That said, you suggested you "hate" teaching. If you really do, maybe it's not for you. On the other hand, you're here asking about it, so maybe you're interested in changing. To do that, try hard to put yourself in the shoes of your students, and remember that they're just trying to get by. Some will fail, and that's okay. But you can help all of them, even those who won't ever get your subject, without resenting them.

Personally I found that it got better as the years went on. It was irritating when students barely a few years younger than me were complaining and begging for grades, but as you get older the students become so young that they're cute no matter what they do!

Also, you need to assess your situation objectively. If by large public school you mean Berkeley or Michigan or others of that calibre and you're one of the strongest grad students there, teaching might not matter so much in your career (it still matters, but there will be other things that make your job worth it) but if you see yourself as mediocre, teaching matters a lot in tenure-track hiring, so you'd better get used to it. Furthermore, even some top tier schools care very much about your teaching records, even at the postdoc hiring stages, so if you do a bad job you're cutting yourself out of some jobs.

Becoming more approachable and bonding with your students (which is much easier to do as a grad student) will also make it more fun.

Yes, you should think more positive about this, and at least don't take it personal.

The students are sloppy, and you have to repeat stuff. This is how people learn, don't be surprised. If they would understand everything the first time they see it, no teacher would have a job. Don't take it personal. Additional tip: if a student wants to have points for something that's clearly wrong, they can go to your supervisor. Don't draw out the discussion.

The students want to have free points. Of course, everybody wants to have free stuff. Don't feel offended, and just grade the way you think is right. There should be no problem telling adults that they're not getting something.

The idea that this behaviour is unfair, offensive or disrespectful is just in your head. You cannot expect everybody to work as hard / be as smart as you are yourself. Think about how bad you would do in a Chinese language course (and what you would ask the teachers if you really had to pass this course).