Since the ecumenical movement was really founded in Scotland, I’m concerned because the Catholic Church has recently closed the only seminary they had there.  Does this mean that the more “ecumenical” we become the less “Catholic” we might become?

In a logic text book, I think that would be called a “non sequitur” (the one does not follow from the other).

As you note, the World Missionary Conference that took place in 1910 in Edinburgh, Scotland, is generally considered to be the launch pad for what is today known as the ecumenical movement. Scotland, however, has by no means been the laboratory for that international  movement; it just happens to be where that meeting was held. So I don’t think there’s any cause-effect relationship between that Conference taking place in Scotland a hundred years ago and a Catholic seminary closing there today.

If we really understand the meaning of the word “ecumenical” and the word “catholic”, there is every reason to believe that becoming ecumenical will make us more catholic.

“Ecumenical” comes from the Greek word oikumene, referring to the whole inhabited earth. It was a secular term that the Church took over and invested with a spiritual content. In the Church’s usage, it referred to all the people in the known world living as members of a common household of faith.

And the word “catholic” means universal, i.e. the faith that is everywhere. When you set the meaning of those two words side-by-side, you see that they’re both describing a similar reality, namely, oneness in faith.

Being Catholic today means being ecumenical, being committed to seeking unity in faith, sacraments, leadership, and mission. The more Christians of every stripe become enriched in their own tradition with what the Holy Spirit has been doing in other traditions of Christian faith, the more catholic they’re all becoming, i.e. the more their particular faith understanding and practice is reflecting the faith and practice that is everywhere or universal. In other words, catholic.