When Jesus founded the Church, it wasn’t a bunch of separate churches with their own individual doctrines, but a body with different parts throughout the world. We can see this from how Sts. Peter and Paul jumped from church to church around the Mediterranean Sea, founding churches that supported each other and had the same doctrine and rules.
It only makes sense that if Jesus founded one Church, it would be for the whole world. The word “catholic” comes from the Greek word “katholicos” which means universal. With that in mind, the Catholic Church is the Universal Church for all of humanity founded by Jesus. Only a single Church founded on Christ can fulfill the Great Commission, baptizing and making disciples of all nations.
One of the most beautiful things about the Catholic Church is its universality. No other Church can claim to have 1.2 billion members from nearly every single country on earth. I can attend mass pretty much anywhere around the world, and though I might not know the language, it’ll be the same liturgy with the same Eucharistic Lord and the same beliefs. Do you really think that a Christian missionary in Mongolia is going to have success asking people if they want to be Southern Baptist? In Mongolia people have nothing in common with the American South. The Church must be able to adapt to different cultures without changing the doctrine or liturgy, which has been shown by the Catholic Church time and time again, on all 6 continents.
The most recent cardinals around the world appointed by Pope Francis give a beautiful testimony to the universality of the Church:
Pietro Parolin, Italy
Lorenzo Baldisseri, Italy
Gerhard Ludwig Műller, Germany
Beniamino Stella, Italy
Vincent Nichols, Great Britain
Leopoldo José Brenes Solórzano, Nicaragua
Gérald Cyprien Lacroix, Canada
Jean-Pierre Kutwa, Ivory Coast
Orani João Tempesta, O.Cist., Brazil
Gualtiero Bassetti, Italy
Mario Aurelio Poli, Argentina
Andrew Yeom Soo jung, Korea
Ricardo Ezzati Andrello, S.D.B., Chile
Philippe Nakellentuba Ouédraogo, Burkina Faso
Orlando B. Quevedo, O.M.I., Philippines
Chibly Langlois, Haïti