Why does one avoids animal protein in kidney stone is it because it will create another stone or consolidate the existing one?

It may have more to do with calcium in animal protein. You should drink enough water daily so that your urine is mostly cololess. This will help in prevent new stone formation,

Specific dietary recommendations can be made only when the stone content is known. Nephrolithiasis or the formation of kidney stones is a metabolic disorder and the tendency to form or consolidate stones remains lifelong. Excessive hydration as suggested by Dr Singh will work against all as creating diuresis, not allowing crystals to precipitate.