If you can't turn the page, burn the book
is a saying that means if you can't make progress where you are then go somewhere else.
If there are problems in a relationship, or friendship, then turning the page means putting the problems behind you and starting a new phase. We need to say that whatever has happened was in the past, and now we are going to move on. We cannot stay on the old page, constantly bickering, or harbouring resentment.
Sadly, people sometimes find this is impossible to do. If they are unable to "turn the page" then they could remain always on the same page, never able to make progress. Then someone may say "if you can't turn the page then it is better to burn the book". This means, rather than stay stuck in a situation where progress is impossible, we may need to destroy the situation completely and move onto a completely new book, perhaps a new relationship or other friendships.
Another situation which can arise is where a person finds he is unable to make progress at work. Perhaps he is seen negatively by management, or perhaps there are simply no openings for progression. Such a person wants to turn the page, to move onto the next chapter in his career. But, if he is unable to turn the page then he may decide to burn the book by looking for a job elsewhere.
There are a variety of contexts the OPs quote could be used. For example, two men may each have been experiencing difficulties with their respective girlfriends. One resolved them and the other did not and ended up leaving her. That one may say to his friend "you turned the page, I burned the book."