It's easy to find better explanations with a quick search, but the general idea is that as habitats change, animals will move toward the poles and come into contact with other species that they historically haven't, creating lots of new opportunities for diseases to jump between species and mutate and do all the things they love to do.

There are also studies implying that animals like rodents and bats that spread the most diseases to humans are also adapting the best to climate change and human environments, which implies increased risk of new diseases: https://royalsocietypublishing.org/doi/10.1098/rspb.2019.273...

There's also the idea of frozen pathogens thawing and infecting animals, which has happened recently: https://www.npr.org/sections/goatsandsoda/2016/08/03/4884009...

In general it's not that climate change makes pandemics worse, but it makes the chance of a new disease infecting a human more likely.