Disagreement is when they disagree with me. Criticism is when they criticize me. Hatred is when they try to belittle and discredit and charge me with all manner of untruths simply because I disagree with them.
I think disagreement is simply when the other person/s say or believe something which I don't agree on - we disagree. It can be mild disagreement or fundamental disagreement.
Criticism - I believe that's when someone points out something negative about you, you are doing or saying something that they believe warrants criticism. It can be constructive or not. Criticism is one I have done a lot of personal development on... I used to be ever so sensitive about - I couldn't stand any form of criticism, Just hated anything negative, even if well intentioned.. Now, because of the particular course I am on, I get criticised or critiqued all the time - and I have come to see it as a positive thing.. Nasty criticism is probably still nasty...
Hatred - well that's a category above nasty criticism. It's usually not about the person being subjected to hate, but more about the person doing the hating. There's something within them that cannot tolerate in a reasonable way people who are different, people who disagree or people who criticise. They are often insecure and feel overwhelmed quite easily.
Ideally, they shouldn't be. I often criticize positions I agree with because I want to test the limits of the argument. And I can do either without hatred.
Disagreement is healthy. Criticism should be constructive, meaning solutions are offered. Hatred is what you find here: Bigoted, bitter, bellicose, prejudiced, inflammatory, discriminatory coarse, vulgar and seething with a lynch mob mentality.