There are a few disadvantages of showing large number of comments on one page. If your website gets a lot of comments then you must have noticed that the comments load slower than other content you have on that webpage and a long list of comments also make the navigation difficult for visitors who are willing to further the discussing by posting more comments. You can make long discussion easy by paginating the comments in multiple pages.
WordPress already provides you the option for breaking comments into pages, you just need to enable it and add the number of pages you like breaking the comments into.
Visit your admin area Dashboard -> Settings -> Discussions page and enable the last option under the section ‘Other comment settings‘ as shown in the given screenshot. You can define the number of comments to show on each page. Set your options and save the changes. After you update the comment settings, you will either be seeing a numeric pagination or you the traditional Previous & Next navigation on comments, it depends on what theme you are using.