An offshoot of the argument that Catholicism was the first and dominant Church in history is the argument that the Catholic Church remains very popular today. Some Catholics even try to extend this argument by trying to say that since Jesus told Peter that Hell itself would not overcome the Church, and the Catholic Church is still popular today, therefore it must be the true Church.
But maybe Catholics shouldn't be so quick to brag about their numbers. We know from the Bible that even 7,000 people is enough for Jesus to say He had successfully preserved His Church, because that happens to be exactly how many of God's people God said had not bowed to Baal (1 Kings 19:18; Romans 11:4). Furthermore, we know that Jesus only needs two people for the Church to exist (Matthew 18:20). In other words, even if there were 2 billion members of a false Church but only 2 members of the true Church, the gates of Hell could still not be said to have overcome the Church.
By contrast, the scriptures clearly indicate that Christianity is generally going to be a minority faith. The scriptures repeatedly discuss a large falling away (2 Thessalonians 2:3; 1 Timothy 4:1), to the point where Jesus is skeptical that He will find faith on the Earth when He returns (Luke 18:8). 1 Timothy 4:1 even continues to verse 3, which calls forbidding people to marry the "doctrine of demons", which sounds suspiciously like the celibacy of the Clergy. Bottom line: A time will come when the true Church is almost absent.
But what's more is that Jesus Himself warned that many find the path to destruction, while only a few find the path to life (that of course being Jesus). In other words, claiming to be the majority is effectively implying your Church is more likely false.
Truth never was a Democracy, as it often loses the popular vote. Appealing to majority is a fallacy known as argumentum ad populum, and it never stacks up against any logical thinker. But when it comes to discovering the truth of Christianity, an extra layer is added, in that not only is truth not determined by how many believe it, but that large numbers of people believing it is often an indicator of falsehood. Thus, Catholics who brag about their numbers are making a logical error and doing so in a way that undermines their own point.