Why can't I stop people from seeing that I've liked them?

The reason you can't stop members from seeing you've liked them is that the Likes feature is about engaging with other members who you are interested in getting to know further. So not allowing other members to see that you've liked them defeats the purpose of this feature. 

However, it's worth noting that when you like a standard member this action is not revealed to them unless they subsequently take out a paid membership. If you like a paid member this action is revealed to them, meaning that they will see your like in their Likes Me folder.  

Learn more about the Likes feature.