Why storing state file locally on your computer may be problematic?

In general, storing state file on your computer isn't a problem. It starts to be a problem when you are part of a team that uses Terraform and then you would like to make sure it's shared. In addition to being shared, you want to be able to handle the fact that different teams members can edit the file and can do it at the same time, so locking is quite an important aspect as well.