[af_vet_1981]

However, as Paul introduced the Gospel to Timothy you would then make the argument that anytime someone introduces the Gospel to someone and they become saved that person is their "spiritual father".

Perhaps you made a mistake here. Please take a second look at the passage in question and reference the translation you are using. All the translations I read show that the Apostle Paul fathered (begot) Timothy through the Gospel.
There is nothing there about introducing. So fixing the assertion to match the scriptures we have "anytime someone fathers another through the Gospel, he becomes his or her spiritual father." That seems to work.

[ealgeone]

If we use your understanding the injunction against calling anyone “Father” remains. Paul did not refer to himself in that manner as is done in Roman Catholicism.