Manga vs Realisim

Differentiate

First, lets assess what the manga or anime-style is like.

The father was shown a group's gallery of foxes, to which he said they were all like anime(even my own art, which kindof led me to do this). 
I can't speak for others but I can speak for BuryTheMaid(another person whose art was falsely labeled) and myself when I say he is quite mistaken.

While anime people and more realistic people are usually easily distinguished between themselves, animals are often not, and have many different styles and these are just a few.

Side-Character Animals

These anime canines usually consist of a round head, two beady eyes, and a small snout with a little cutie smile, like so;


Little facial detail and basic general-shape anatomy. Still cute tho.

Ginga Densetsu Weed Animals

Bulbous anatomy, boxy paws, boxy snout, and wide human eyes, like so;

_{don't piss it off tho}
Hate the style, love the anime.

Fruits Basket Animals

Little to no detail with minimal shading and near lifeless eyes.


Again, hate the style, love the anime.

Princess Mononoke Animals

A sound amount of detail, gorgeous animation, though human-like eyes.

Wolf's Rain Animals

A sound amount of detail, iffy anatomy at times, as animation is hard work.

and can you believe it? ITS ANIME! :U

THESE ARE ANIME ANIMALS

Acceptance

Manga and anime alike have specific goals throughout their works, set in the very first episode or pages.
Some are made to be beautiful and creative while others are meant to tell a story and enlighten you with interesting plot-twists and thought-provoking events.
Some series are simply not designed to look photo-realistic like you seem to want them to look(plus it would make it vastly more difficult to produce).

These pieces are not more or less, but simply different and shouldn't be persecuted for their beloved creativity.

It is admirable that you wish your daughter to advance in her talent, but to enforce your own preferences onto her is simply pressuring and stressful.
Find out her own quest before simply laying one out to her.
If she seeks to draw photo-realistically, point out anatomy flaws and offer constructive criticism rather than simply saying "Eh, it looks like some anime shit.".
If she wants to draw a similar style to anime, then let her do so. As I said, it is not less, it is not more, it is only a different style from what you like. Simply. Different.

And there is plenty of time to allow her to explore all the many possibilities.

Personal Experiences

Now, this friend of mine isn't alone in this;