The research about the mineral and energy content of breastmilk is here www.who.int/nutrition/publications/infantfeeding/9241562110/en/index.html.
It is the WHO report on the nutritional content of breastmilk and points out that the iron levels in a breastfed baby drop off slowly after 6 months not 3 months, I draw your attention to the last paragraph in the section on iron levels on page 36. It clearly refers to the second half of infancy, that is 6 months plus.
The overloading the gut comments given previously are also somewhat scientifically dubious, if you wish to read all about food allergies and the link to the undeveloped human gut check out "Pediatric Allergy Asthma and Immunology" published by Springer, look at chapter 9, its available as a Google book.
This comprehensive review of the literature on the subject clearly states that in "infants of a few months old" the levels of immunoglobulin are low and thus exposure to macromolecules (large food molecules) in the blood is more likely to sensitize the infant to the food. The large food molecules get to the blood more easily in infants because there are larger gaps between the intestinal epithelial cells. This has nothing to do with the lumpiness of the food as someone said earlier but the stuff the food is made of, different proteins.
In plain english, feed your baby solid food too young (or liquid cows milk) and you risk them developing a food allergy and subsequent linked disorders such as asthma and excema because the digested bits of food trigger the immune system in a way that doesn't happen in older kids with more developed immune systems.
This is an ongoing area of research and some scientists (I've seen one paper on this) have argued the opposite saying that delaying exposure to solids well past 6 months can actually increase the likelihood of allergies as you haven't primed the immune system through a gradual exposure to quantities of these proteins. Breastfed infants get some of these proteins all the time from their mum's diet which is why some babies get intestinal problems if their mum has a sensitivity to cows milk and eats dairy products.
The point of BLW is that human infants have evolved so that their manual dexterity (food handling ability) goes hand in hand with their guts and immune system's ability to tolerate solids and the associated proteins that get into their blood. Giving puree to a 4 month old who cannot hold food, chew or swallow solid bits is introducing food at an age when the baby's gut and immune system are not ready for it. Waiting until the child can handle their own food and feed themselves at a couple of months or so older reduces this risk as (so the theory goes) humans have evolved successfully to cope with digesting solid food when they can get it to their mouth, chew and swallow it by themselves.
Allergies can be triggered by a huge range of foods (pork, berries, citrus, wheat, dairy, eggs, fish, shellfish, food additives, literally hundreds of things). Cows milk is a well researched trigger but not by any means the only one. The reason everyone makes a big deal about cows milk is because people used to feed it to small babies instead of human milk.
At the risk of sounding really up my own arse here, if you don't understand the science contained in these documents linked above you should not be giving advice or opinions on these things to anyone.
P.S. The NHS guidelines clearly state exclusively breastfeed for 6 months then introduce solid foods, they have information about giving babies finger foods and purees. I have their booklet in front of me. BLW is not therefore contradictory to government advice.