There are a number of reasons why some parents allow their children to overeat or to eat food that is full of calories but which may well not be particularly nutritious.
These include:
That is the sort of diet they had during their own childhoods (and they may be overweight themselves).
They may have grown up seeing food as a comfort or a reward.
They may feel that denying a child extra helpings is being unkind or depriving it of love.
They may not fully understand what a balanced diet is.
They may be eating too much convenience/fast food because they have limited cooking skills.
Equally, there are a number of reasons why some children are anorexic, including:
Genuine concerns about a child's diet have led to mealtimes increasingly becoming a "power struggle".
Parents are over-controlling and children feel that denying themselves food is the only way for them to maintain some control.
There are underlying problems in the family that cause stressful mealtimes.
Parents who constantly worry about their weight and go on diets, thus creating anxiety about obesity.
However, the issue of eating disorders is, as someone else said, a very complex one and is likely to include societal factors (e.g. the intense marketing and wide availability of unhealthy foods - which are often presented as being "healthy", and the introduction in the 60's (I think) of the concept of between-meals "snacks"), and may also include certain genetic factors.
Even if parents exacerbate the problem, I find it difficult to believe that the majority of them don't care that their children's health is at risk and I feel the "blame game" is not very helpful. I don't suppose there are many (if any) parents who can honestly say their parenting was without fault.