You're right that we keep getting contradictory information, but the problem often isn't that the studies are bad in themselves, it's that the reporting on the study is bad.
One group does a study that shows a correlation between diet and "brain shrinkage". That's all. One study finds some kind of statistical correlation. Further study is needed. First, the study should be replicated before really trusting the results. Someone would also have to hypothesize what the causal link is, and then study that, because (sorry, I know it has become a cliche, but...) correlation does not equal causation.
But ok, let's assume for the sake of argument that it's determined that the exact diet described here as the "Mediterranean diet" prevents "brain shrinkage". Ok. Now what? What is "brain shrinkage"? Is brain shrinkage bad? What are the negative effects of it? Are their positive effects of brain shrinkage? Oh, and are there other negative effects of the Mediterranean diet that outweigh the benefits of preventing brain shrinkage?
Nobody really knows. I'm sure an expert could provide some information in response to their answers, but they won't have a complete answer.
But reporters don't necessarily understand all of that, and in any case, that kind of nuanced and intelligent reporting won't sell ad time on CNN. You know what will grab people's attention? The headline, "Drinking olive oil will make you smarter!" So that's what they report, and suddenly the common wisdom is that we should all be guzzling a gallon of olive oil per day.
And then a few years later, there will be another study where there's some correlation between olive oil and an increased risk of some particular rare form of cancer. There will be all the same uncertainties and complications of interpreting the results of the study, but reporters won't report on the complications. There will just be a headline, "Olive oil causes cancer!" Now everyone decides we're supposed to cut olive oil our of our diets.
Science may eventually find that the studies themselves were flawed, or the results were misinterpreted, or the correlation was just a statistical anomaly. Or we may eventually find that there is a correlation, but the causal link is something unexpected. Maybe people who cook with olive oil are less likely to eat butter, and butter causes brain shrinkage. Or, it's possible, just possible, that olive oil does in fact help to prevent brain shrinkage as well as increase the risk of a rare form of cancer, but that it does each of these things to such a minor degree that it's not worth considering when choosing what to eat.
It's also true that some studies are bad. Unfortunately, we don't put much priority on repeating studies to confirm results. However, the far bigger problem is that most of our news outlets suck. Even the respectable ones like the BBC and New York Times are just awful. Honestly, I'm not sure how to improve them, because another big piece of the problem is that *we, the audience*, suck. We insist on clicking on clickbait, watching tabloid junk, and superstitiously believing whatever our chosen news outlet reports.