Female breasts have fat in them, too. I think about 2/3 of the average female breast is fat, in fact.
What having moobs meant for me was that at 5 days on HRT, I suddenly had perky, visibly female 40A-cup breasts. 😉 Basically, as soon as I had breast buds, everything perked up and starting looking breast-like. I have NO complaints about having a bit of a head start. Also, moobs can be a sign of a body with overactive estrogen receptors and/or a lot of circulating estrogen - meaning a body that takes to HRT unbelievably well.