We Byzantine Catholics are in the middle- dismissed by Roman-rite Catholics and disrespected by Orthodox. The middle is a very difficult place to find oneself. Should we just align ourselves with the Orthodox; our Liturgies are basically the same. Or should we just give up our rite so that we can be accepted by the majority and remain under the authority of the Holy Father? It is my experience that many ex-Protestants who want a more theologically sound religion end up with the Orthodox; there isn't that 'problem' of submitting to the Pope. On the other hand, the Roman-rite is big and well- established. Why bother with the small Eastern rites of the Catholic Church?
Why bother? The answer is in the name of the Church- Catholic, meaning universal. This doesn't simply mean that the Church embraces different colors and cultures. It embraces- or should- different rites. If I had a dollar for each time a 'good' Roman-rite Catholic ended a long conversation over the Byzantine rite with, "so, you are Orthodox"- I would have a lot of dollars!
So we Byzantines are in the middle- fully Catholic and fully Eastern.