I'm sorry you're having trouble with this recipe.
In general you might have this result if the cake is overmixed and/or the butter is underwhipped.
Over mixing (after flour is added) builds gluten and undercreaming the butter/sugar blend doesn't add needed air to mixture. Also, be sure to beat a little after after each egg.
Once you begin adding the flour, mix as little as possible.
Here are some trouble shooting tips for cakes that might help : Butter Cake Troubleshooting - Joyofbaking.com *Tested Recipe*