Amino Acid requirement + intake in relation to diet + meat type
There is a difference between animals in their requirements for amino acids. For example, cats need high amounts of taurine (and can't make it) and when fed diets lacking enough can go blind. This is why vegans trying to feed vegan diets to their pets can be very bad for the pet. Animal proteins have sufficient taurine for the cat.

However, the meat of a cat or dog is just as a complete source of protein for humans as any other meat. All essential amino acids are there in sufficient ratios. Suggesting otherwise by her father suggests some confusion between the dietary needs of cat vs. the nutritional value of the cat to another predator.

Your second question is easily answered by looking up essential amino acids.  Wiki is plenty sufficient to get the gist Wiki Link. In short, most plants don't contain the full complement of amino acids that humans require (and can't make on their own). So to get this full complement, it requires eating multiple plant products that together contain the required amino acids.

From Harvard School of Public Health


  Protein is built from building blocks called amino acids. Our bodies make amino acids in two different ways: Either from scratch, or by modifying others. A few amino acids (known as the essential amino acids) must come from food.
  
  Animal sources of protein tend to deliver all the amino acids we need.
  Other protein sources, such as fruits, vegetables, grains, nuts and seeds, lack one or more essential amino acids.
  
  Vegetarians need to be aware of this. People who don’t eat meat, fish, poultry, eggs, or dairy products need to eat a variety of protein-containing foods each day in order to get all the amino acids needed to make new protein.