The first step is trying to understand what specific ingredients taste like...
The best way to understand this quickly is by comparing commercial beers that you like with homebrew clone recipes for those beers. You can pretty easily pick out certain ingredients (like biscuit malt in Fat Tire), specific very unique hops, etc. Other malts are often more difficult to nail down, but looking at styles that really feature specific specialty malts (scotch ales, red ales, amber ales, porters, stouts, etc) and comparing them to clone recipes can help. And of course learning the differences between different yeasts is important, but if you're sticking with basic American/English recipes, starting with a good dry yeast like US-05 or S-04 is a good way to focus on the malts and hops.
From that, you start to get a sense of what ingredients actually do in a recipe. So you imagine "what do I want this beer to taste like", and work backward from that to "what ingredients in what proportions will give me that?"
At this point it's best to start looking at as many homebrew recipes as you can. Let's say you want to make an amber ale. Look at a bunch of amber ale recipes. Get a sense of what the *general* proportions are. Create a general recipe that's an amalgam of those that you spot, and only then do you start looking at what you might want to change about that amalgam recipe.
The truth is that it's not rocket science. Unless you start deciding you want to be Mr. Experimental and go way off the reservation with wild ingredients and don't pay attention to basic brewing tenets, you'll end up with decent enough beer. And as you refine your palate and your knowledge of ingredients, you have the capability of getting really good.
That said... I honestly believe that some people have more natural aptitude for this. I liken it to the "cook vs chef" mentality. There are some people who are amazing cooks. They see a recipe, they can nail that recipe through process and technique, but if the recipe isn't good, they can't always figure out how to change it to make it good. That's the chef skill--the ability to break down the recipe, understand *why* everything works the way it does, and know how to adjust it to get the right result. If you at some point decide that your own recipes aren't for you, and just stick with tried-and-true recipes found in books or online, it doesn't make you less of a brewer. If your beer tastes good, no matter where you got the recipe, that's the mark of a good brewer.
One more thing -- if you're going down this path, you should ABSOLUTELY stop buying kits that don't tell you what's in them. Personally when I jumped to entirely making my own recipes (about the same number of batches you've done), I just stopped buying kits and starting buying the individual ingredients. But as you develop your palate, you can still use kits, as long as you know the recipe of the kit so you can understand WHY the recipe makes the end product.