Dogs chew on tissue paper sometimes if they are bored, and sometimes they chew paper for the taste or texture. Some dogs just like ripping things up.

If eating tissue paper is a regular occurrence and not just something the dog does occasionally, then it is possible that the dog has pica. Pica is a condition that also affects humans and results in a urge to eat things that are not edible. Eating excessive paper can be bad for a dog's health in the long run because paper can get stuck in the dog's digestive system. This can eventually require surgery, so eating paper should not be encouraged.