Some people are patient and others are short tempered. What makes these people develop those types of personalities?

There is no definite answer to this but result is due to multiple factors like environment , type of education , level of maturity based on various life experiences etc. Lot of training that organisation provides depending on job roles also make person have level of patience or short tempered. For example ; a customer service executive is expected to have good amount of patience to manage various situations and being / expected to be trained that way and hence recruited accordingly. Labour intensive organisation supervisors need someone with little bit of short temper to get things done and boost productivity