Well, it is strictly speaking an inference. There is no scripture that says “Mary was free from sin and had no other children”. We are supposed to think as well as read, no?
This is just as much an inference as the Trinity is the inference. There is not scripture that says “God is one in three Persons”. The idea that unless there is a clear scriptural prooftext is itself am extrascriptural, in fact, counterscriptural inference.
You are incorrect that the sinlessness, as well as perpetual virginity of Virgin Mary is not held by the Orthodox. They have objections to the doctrine of Immaculate Conception. Their objection is not based on what is ar os not stated in the Holy Scripture, but rather to the manner in which it was adopted by the Church in Rome. At times, they also miscast the doctrine, which is unfortunate but has nothing to do with our argument here.
I agree that the doctrines must be checked by the Scripture. That happens to be a Cathoic teaching as well.
Unless that doctrine is ex cathedra, such as the eternal chastity of Mary, or her sinless nature. According to the Catechism there can be no question; the debate is over.