Anti-Catholic bigots at Michigan like Fielding Yost and Fritz Crisler were able to get the then Western Conference to reject multiple ND applications for membership.

They also attempted to get their conference mates to blackball ND football.

This caused ND to compete as an independent. Knute Rockne got the idea to barnstorm all over the country by train, play Southern Cal and the big boys of the time anytime/anywhere and...

...the rest is history. Michigan and the Big Ten are the reason that ND was always a football independent (until this year).

After ND became a national power and TV/attendance draw, the Big Ten then chased after ND.
ND told them to pound sand.

ND could make $25 million as a Big Ten member but has refused multiple invitations.