Starting solids

I went for my baby's 4 month shots and my pediatrician (who has already expressed disapproval of my birth center delivery, my weight, and my baby's weight) insisted that I should start solids now.

I'm not sure if I'm comfortable with that, and so much that I've read says it's best to start at 6 months or so. She's ebf right now, and doesn't even like anything not-boob-shaped in her mouth. What's the hurry? Are there any significant benefits to starting early?

For the record, she was born small, has been gaining an acceptable amount of weight regularly, I produce plenty of milk, and I was very small pre-pregnancy.

When is it best to start?