Wth is being in relationship but should be independent?

It mainly deppends on the about.
Some stuff is mainly individual, but not all of it.
Some stuff is or should be of the domain of the team according to the kind of partnership you find of value.

Maybe not being tied-at-the-hip 24/7 kinda-thing? Having your own circles of friends and interests as well as sharing them?

I think for most, it's being able to do things on your own without having to constantly be with each other. It's a common sentiment for the current age where many couples are two people working towards individual goals rather than a shared vision. They are together for companionship, but not necessarily to work towards the same vision.

For some, they have just been burned by people they feel are too clingy. Like the type of person that doesn't let them hang out with friends or engage in personal hobbies by themselves.

Context and background knowledge tend to be important for determining what the person is actually trying to get at.

Even i have secrets that i must take to the grave...

Relationships in which one partner is entirely dependent on the other have a higher tendency to become abusive or toxic or whatever.