Heat olive oil in a large nonstick skillet over medium heat. Add garlic and cook for 30 seconds until fragrant.
Add spinach and cook, stirring frequently, until wilted, about 2 minutes. Season with a pinch of salt and pepper. Transfer spinach to a bowl and set aside. Wipe the skillet clean.
In a bowl, whisk egg whites with remaining salt and pepper until frothy.
Return skillet to medium-low heat and pour in half of the egg whites. Cook without stirring for 1 minute, then gently push cooked edges toward the center with a spatula, tilting the pan to let uncooked egg run underneath. Cook until just set, about 2-3 minutes total. Slide onto a plate and repeat with remaining egg whites.
To assemble, lay a tortilla on a plate. Top with half of the cooked egg, half of the spinach, and half of the feta. Add avocado slices if using. Roll up tightly, tucking in the sides. Repeat with remaining ingredients.
Serve immediately, or wrap in foil for later. If desired, warm the wraps in a dry skillet for 1 minute per side to soften the tortilla.