I am out in the wild area and I keep finding random Pokémon that are marked as being “very strong”. I’m normally able to defeat them but I can never catch them. It always tells me the Pokémon has their guard up and I can’t throw a pokeball to catch them with. What are you meant to do here in order to catch them?
You need to get more gym badges. When you defeat a gym leader you will get a badge and it will tell you that you can now catch Pokémon up to level X. In your case, you do not have enough gym badges to catch the level of Pokémon that you are currently battling against.
For theoment, all you can do is battle them for the do points. Grind up some levels and then go get the gym badges so you can come back and catch them.