Please explain reasons why there is no pain in periodontitis?

Acute vs chronic. acute infections happen fast and produce pain usually because there is pus pressing on a nerve and there is a big immune response. Periodontitis is a chronic slow going infection that usually does not produce large amounts of pus and the immune response is different.
Low grade infection. Periodontitis is a low grade slowly progressive disease which causes the loss of the bone support of your teeth. You can have pain if tooth roots are exposed and become sensitive or if the pockets around your teeth develop secondary infection. You should have it treated in the early stages to prevent the loss of your teeth.