Let me elaborate:
The
principium contradictionis or Principle of Contradiction -(P ^ -P) is a theory of Logic proposed by Aristotle in his Metaphysics.
In simpler terms:
If A is not B
than A can be or not be partially B at the same time.
But A cannot equal B at the same time.
(Not completely correct, but best way I can explain it in layman terms) Basically a Basketball can be partially like a Baseball because both are round and are used for Sport, however a Basketball cannot be a Baseball at the same time because fundamentally they are mutually exclusive.
Aquinas being a better Aristotle than Aristotle

decided to apply this theory to defense of the Catholic Church that is other religions can have portions of the truth, however since only one institution can contain all the truth than only one Church could be completely right. Being a Dominican Friar it’s pretty easy to assume which Church he saw as the Church
However the theory makes sense, if the Catholic Church was at one time the only Church, then some Churches derived from Catholicism can contain partial truths. However because the Catholic Church cannot equal the Lutheran Church (for example) at the same time, it’s logically impossible that two mutually exclusive things can be exactly the same. And because there is only one solution for every equation (The true Church is = ?) that is why the Church you associate with is a big deal.