Did you grease & flour the pan before adding batter? Were you trying to take the cake out of the pan as soon as it is removed from the oven? Were you letting it cool (much) more than 10 minutes before trying to remove it? Those usually are the reasons a cake breaks when removing from pan.
You don't need parchment paper - waxed paper; a brown paper bag or other such would do just as well
Grease and flour the pan, put in which ever paper you are using, and grease & flour that before adding the batter. Sprays such as Pam or Baker's Joy can be used.
Once the cake has baked, remove it to a slightly elevated rack to cool in the pan about 10 minutes, then turn the cake out of the pan onto the rack to cool more. After about 20 minutes loosely cover it with plastic until completely cooled thru.