The teaching and dissemination of Torah is perfecting oneself and his fellow man because the Torah, being the blueprints of creation, is also the handbook or guide for life itself. Imagine you were a doctor and you walk onto a battlefield strewn with injured men, and worse. Some are sick, some have lost limbs, all are in pain and agony for not being in a healthy state. You are pained and sickened at the sight but you can’t turn away. If you have the ability and tools to help them recover, you must tend to them. You must heal them. You should feel empowered to do whatever it takes to get them back to perfect health when you can.
This is all the more true for one who has the wealth of Torah under his belt. The Torah is what brings us to perfection since it was created by the Almighty, and any part of the Torah which one learns brings one closer to perfection. Therefore, living in the battlefield of life, among others who are more and less perfect than you, one must feel compelled to perfect oneself and, in turn, perfect others, when he or she has the tools and ability to do so.
The Ralbag said this is the method that Hashem uses to spread the instruction booklet of life. Not with humongous billboards or pamphlets dropping from heaven, but with teachers teaching what they were taught from their instructors, going back for generations from when Moshe received the Torah from Hashem. Since this is the method to perfect humanity, anyone who has the proper means to contribute to the perfection of the world should feel, and is, obligated to do so.