Some people, who I know, like to tout the “personal relationship” mantra. I believe that we all need a personal relationship with Christ.

I see nothing in the Catholic Church that discourages that relationship, I feel closer in His Church.
The problem starts when “personal relationship” means “you can’t tell me how to do it”. This can become another rejection of authority, rather than a closer walk. Not everyone uses the phrase this way, but I know a couple of people who do.
The other problem that comes from the “me and Jesus” idea, suddenly anything that involves tradition seems to block the “personal” aspect. They may no longer need to seek out others in church, or may reject church traditions altogether. In my parents lives, it became “I don’t need a church to be a Christian”.

OTOH, it can become license to judge traditions as “empty”. We must always be careful not to judge what we do not know. Even if some traditions may seem “empty”, we do not know how it moves in other peoples’ hearts.
I believe that the attitude of " Not dependent on a church, only on Christ" stems from rebellion. We want our own way, so we rationalize our ideas. When we stop trying to submit to Christ, we can fall into many traps that let us have our “own way”. Many people are raised in this “do it your own way” church philosophy, so they are blind to the beauty of the Church and Tradition. This may explain why we see so many “independent churches”. The whole idea of “independent” churches would have seemed ridiculous to the early Christians.