It was probably the father who decided that Antonio should be a priest. It was common for a poor family to ensure at least one child the "privilege" of a free education and respect for a defined social position. Thus, Vivaldi began his education for the priesthood at the age of 14 and was ordained a priest about ten years later.
Only a year after his ordination, in 1703, Vivaldi stopped saying Mass regularly, declaring that his health did not allow him to do so. If this was true, it must be understood: but it is now a tradition that Vivaldi's cassock was tight, being much more attracted to the musical profession.
In short, he was certainly ill, but perhaps he exaggerated his conditions a little. Even with some unproven conjectures (Giovanni Legrenzi as his Maestro) who started Antonio, from an early age, to study the violin has been his father.