Coffee brewed without filter taste less bitter and sour? So my roommate and I have been a bit intrigued by brewed coffee after watching tokyo ghoul (lol)

We got some BonCafe grounds(southeast asia brand) at a supermarket and brewed it with a filter. Have to get sugar and milk inside.

He bought some whole beans (looks medium roasted) and grinded it and also drip brewed it. Even more bitter than the seemingly darker BonCafe.

And in Aeropress with a AbleBrew disk fine metal filter it taste even more bitter and sour than the drip brewed variants.

Then I got an idea from turkish coffee where you directly mix coffee grind with water without filtering. (well there is further boiling involved in turkish coffee but whatever)

Then after pouring in water and mixing it with coffee groind with a spoon for like 10 seconds, and letting the ground set, it tasted (to me and him) surprisingly better than drip brewing and aeropressing.

And to me there is coffee taste inside.

Recently I got some old (2014 September) lavazza qualita oro ground coffee, tried aeropress and direct mixing, same thing happened. 

So is that the “what you are supposed to get from coffee” taste quote the connoisseurs? Or is it underextraction or something? But why isn't I seeing any recommendation on this brewing method? Am I doing anything wrong with the aeropress and drip brewed ones? (to me they taste both sour and bitter)
I'm not exactly sure if this is accurate, but I think it has to do with flavor extraction. 

When you brew with a filter, the water is going to fall through the grounds too fast to actually develop good flavor. Sure, you'll get coffee, but you're only giving the water enough time to take the more bitter tastes with it. I have this same problem with my coffee.

When you brew directly into water, all of the water is in contact with all of the grounds for a considerably longer amount of time. The water will extract the bitter tastes AND the more flavorful aspects of the grounds, which is why you thought this tasted better. It wasn't just bitter, it was bitter and flavorful, and that's coffee.

You're not doing anything wrong with the filtered methods, it's simply a matter of opinion among coffee tasters. Some people enjoy the convenience of fast, filtered, and bitter coffee because it's what they know as coffee. The reason the Turkish method isn't suggested is because, the way you describe it, it sounds like the grounds stay inside the coffee, and many people loathe having to deal with that--even though it produces much better coffee.

So no, you're not doing anything wrong; however, the reason you're finding flavor differences is that the extraction of flavors is far different between the two methods!