As I found out I was exerting force towards the center of the cap while trying to twist it around. For bigger hands this is a problem because you will be exerting more force in compressing the cap rather than twisting it >_<. It seems I have found the answer why smaller hands do better in opening bottles, such as soda and ketchup.
I sat down and looked at the bottle for a few minutes. Can this be solved without googling it? Woooot! I was able to solve it, take a look at the image below, hehe. To be able to open the bottle it would be better to apply two twists on it, one at the cap and a counter-acting one at its body. What this does is you will be able to multiply the effort in trying to open the bottle. I also thought that it kind of heats up the inside of the bottle which should expand it a little bit. Also shaking the bottle might do so but I do not think that it helps out a lot c(”,)
+1 Post! lol