If you feel called to teach, why not look around at some other orders?
A vocation is a call, in this sense a call to a way of life that allows one to more fully love their neighbor (and, by extension God and His Holy Church).
The FSSP is a Society of Apostolic Life whose main charism is the promulgation of the older rites through parish communities. While this may include teaching, it is not directly part of their charism.
If we go by the FSSP’s official literature, one may feel that their vocational call is pointing in that direction if they feel a strong desire to bring God’s love and healing presence to those who felt wronged by the liturgical reforms, or for whatever reason have a strong attachment to the older rites. To join up simply because of an inordinate desire say the mass in Latin, according to the old rubrics, would be to completely ignore the point of a vocation in the first place.