Did most pandemics originate from Asia/China?
According to Merriam-Webster Dictionary a Pandemic is:

an outbreak of a disease that occurs over a wide geographic area and affects an exceptionally high proportion of the population : a pandemic outbreak of a disease

Epidemics are considered a smaller scale version of a pandemic affecting a smaller region, community or population. Epidemics are obviously more common than Pandemics for that reason.
COVID-19 is believed to have become a pandemic event because it has affected multiple continents and most if not all Nations of the world. These extent of pandemics though rare in the past may become increasingly frequent as our world continues to become more globalized if further precautions are not continuously developed.
According to this list, Around 5 of the world's Pandemics have likely started or been mainly spread from and within China, They are:

Third Plague - 1885
Asian Flu 1957
Hong Kong Flu - 1968
SARS 2002
Coronavirus Disease - 2019

These are 5 out of the 20 pandemics in the list. Would that count as a majority? Depends on how you look at it. For one country to start so many does make it unique and a possible majority but we must also consider the size of the country's population relative to the rest of the world. For such a large country (currently 1.4 Billion people which is about 18% of the world's population) with a large portion of the population being poor it is almost expected that China suffers more epidemics than most countries.
Pandemics and Epidemics start for a wide variety of reasons (some quick-search articles that explain: 1, 2, 3) and many of these pandemics develop because of unique environments or pathogens existing in 'coincidence' with each other.
Generally, lack of hygiene, low economic wealth, lack of healthcare products including vaccines coupled with a high population are common societal trends for the beginning of an epidemic. However the pathogens have their own characteristics that make them effective at causing an outbreak. This includes but definitely is not limited to: rapid mutation rate, easy transmission such as through air (e.g. SARS) or water sources (e.g. ebola virus), and zoonotic capabilities (being able to infect more than one species such as swine flu).
Two sources that must be strongly suggested to check out for anybody interested in these sort of topics are the Center for Disease Control and Prevention and the World Health Organization