Hm, that’s not a Catholic position, actually. The idea that the self is to be eliminated or “seen to be imaginary or non-existent” is a notion taken from modern strands of Buddhism. It appears nowhere in Catholic teaching, not even implicitly. Catholics believe there is a self, typically called the soul, which truly does exist, is eternal, and is very, very much worth saving from perdition. In fact, that’s pretty much what Catholicism is about from beginning to end, and most other religions too.
As for the cross, it’s got nothing to do with eliminating the self. The cross is to stand condemned when you are (or have become) the embodiment of innocence and perfection, like Christ.
Of course the type of person you describe is distasteful – that I don’t disagree with, and indeed self-help mantras of the type you describe are unhealthy, as is the current obsession with taking one’s own picture. But such things do not flow from the true self; they flow from vanity, which is an aspect of pride – first of the seven capital sins.
Which leads me to another way of putting the difference between what you say about the self, and the Catholic position: the Catholic position is that man’s essential problem is his sinfulness, not his sense of self.