One day is not a failure. One meal is not a failure. One bite: not a failure. Each time you put a food in your hands, it's an opportunity to choose.
I love these statements because they are absolutely true.
As to the OP: Declining a dining invitation in the early stage of this journey is not the end of the world! You can ALWAYS go out with friends, coworkers, or family at a later point, when you're comfortable making the appropriate choices at a restaurant. Sometimes, at ANY point in the journey, being faced with temptations is just more than we can handle right then, so the best choice is to decline the invitation.
I, too, LOVE pizza. I made a conscious choice when I began, to allow myself a pizza at an event about 10 months away - IF I stayed on plan until then. Was it difficult? At times, yes. But I made that "date" far enough in the future that it likely wouldn't pull me completely off plan at that time.
Now, however, I actually enjoy a low-carb pizza as much as one with a typical crust PLUS I know exactly what ingredients have been used to make it.
Atkins is a plan that you need to work consistently for best results. Stay the course; believe that you are worth this effort. Good luck.