All protein is not created equal. Each source of protein has a different amino acid sequence profile. That goes to say that eggs will be higher in certain amino acids than beef and vice versa. Since we all eat protein, essentially for the amino acids in which they contain, this becomes important. However, if your ingesting your protein from complete protein sources like dairy, eggs, beef, poultry, and fish your receiving a wide range of all the amino acids you need. Eating a majority of your protein from incomplete sources like plant based proteins (veggies, grains, and legumes) could leave your diet lacking of certain amino acids.
Would you not grow if you did not recieve certain amino acids?
Yes leucine in particular.
As well as others. The body is very complicated and if a person was missing/diffecient in a certain amino acid, this may prevent them from synthesizing other types of amino acids (because enzymes in the body are made of protein). This can of course lead to many different problems with both growth and health.