Me - no eczema
dd1 bf till 5yo moderately severe eczema.
dd2 still bf at 2.5yo. v mild eczema.
main difference, moderate allergy to egg and mild allergy to dairy which I was consuming (egg but not diary)till she was diagnosed with at 2.5yo. She was also getting dairy in other places in her diet though. I stopped eating egg and eczema cleared up significantly. I suspect with 2 allergens others untested still existed plus environmental factors were at play here.
dd2 is not allergic to egg or dairy.
most importantly, pronounced history of eczema on paternal side of the family including, I believe, egg allergy which no one in the family had been diagnosed with but from family stories, I began to suspect.
So genetics play a big role in eczema. However, I would not do anything different, knowing what I know now. I have faith that without breastfeeding her eczema would have been worse. In fact, she was starting to develop asthma at 2yo which made me push for allergy testing. Breastfeeding made parenting an uncomfortable child easier.
Also I went with breastfeeding because I was scared of diarrhea and vomiting in babies which is much more prevalent and for which the evidence for breastfeeding is robust. I work full time and they attended/attend nursery full time and while they have had the odd icky nappy, neither have ever suffered a bout of D&V despite exposure to many children who have. In fact, at nearly 6, dd1 had her first vomiting episode and did not know what it was and how to react to it.