Probably the most common who have something to say to the mod team are those who blame us for pushing an agenda. We welcome and encourage debate. We want people to call bullshit on something bunk, but we stand by that it has to be something that can be substantiated. We just want you to provide some kind of proof, source, etc. other than, "This totally happened to my sister's boyfriend's cousin!"
Some people take those removals very personally, because the comment is about something heavy that has greatly impacted that person's life. They feel like we are snubbing them when they took the time to reveal something personal. A non-real example would be a study that shows that cancer survival rate increases when you drink at least 60 oz of water daily. Someone will inevitably reply with, "My mom died from cancer, and all she dra nk was water with the occasional cup of tea." I mean, we're sorry for your loss, but your single anecdotal point doesn't really refute the claim. The comment gets removed, and then we're called monsters. If you really think it's bullshit, find another study that claims otherwise or poke holes in the study itself.
Another common one reason is low effort comments or comments that don't add to the discussion. "Jeez, why is this a comment graveyard?" is a pretty common removal. There usually aren't hissy fits, but this, jokes, puns, lyric chains, comments like, "Yeah and water is wet," are also common. Two other low effort comments are, "Someone give me TL;DR please," or, "I want to believe this, but some comment is going to blow this claim out of the water."
The reality is that most removals are boring.
This one annoys me when I see it somewhere like /r/Science. It's like, the miss make it super clear that they remove low grade /off topic comments etc. It's not that hard to understand.