It is important to understand that there are 'healthy fats' in ALL whole foods!  For example:

1 c. of raspberries contains 16% of your daily value of omega 3's

1 c. garbanzo beans contains 15% of your daily value of omega 3's.  

Zucchini is 16.1% of calories from fat and contains 8% of your daily value of omega 3's in 1 cup

1 cup Spinach is 14.3% calories from fat and contains 4% daily value of omega 3's

Fruit contains fat as well, albeit less than vegetables, but it does contain a small percentage of essential fatty acids, generally around 1-2% per fruit.  

As you can see it is very, very easy to obtain all the essential fatty acids your body needs from whole plant foods even if you do not include any nuts, seeds, avocados, olives or coconut.  All whole plant foods contain all the nutrients the body needs and you do not need to choose specific foods for protein or essential fats.   

While avocado, nuts, seeds and other plant foods high in fat are whole foods and do contain high amounts of essential fatty acids they are also very high in calories which can hinder weight loss in those who are struggling with their weight.  Fat is 9 calories per gram, whereas protein and carbohydrates are only 4 calories per gram.  When you more than double the amount of calories in the same volume of food it can and does significantly impact weight loss.  There are individuals who can consume these foods and do not have weight issues and that is perfectly fine but for individuals struggling with serious health conditions and excessive weight it is best to avoid these foods for optimal results.  Hopefully that helps you understand where essential fats come from and that by avoiding nuts, seeds, avocados etc... it does not negatiavely impact your ability to obtain all the essential fatty acids your body needs.