It isn't ethical to lock people up and feed them a steady diet of something we might thing is going to cause them to develop some disease. So we have to rely on mostly self-reported data collected over extended periods of time.
That being said, I think the first pushback against eggs had to do with their high amounts of cholesterol. It was original assumed that dietary cholesterol intake was related to blood cholesterol levels. Which is something we now know to be false.
However, eggs are very high in saturated fats. The American Heart Associate still recommends that these be limited (from all sources) because there is a good deal of evidence that saturated fat intake contributes to elevated LDL cholesterol.
I generally trust AHA recommendations, but they are not free from bias, as they have food companies as "corporate supporters."
An article by Glenn Greenwald (of interviewing Snowden fame) on Ag Gag laws [1] made me realize that, at least in the US, eating bacon meant I was supporting some real fucked up shit.
I'm not opposed to meat, I just bought a whole beef, but I definitely took a hard look at where my meat was coming from.
[1] https://theintercept.com/2017/10/05/factory-farms-fbi-missin...
Edit 1. My comment was made on a submission, which I did not think would gain much notice. Oops. Low quality comment to the fore!
Edit 2. Really though, I eat a couple of eggs a day. I should scale it back anyway, as a hedge, and eat non-traditional (In USA) breakfasts, like rice and beans.