I'm not sure my attempts at breast feeding have any purpose beyond making me feel like I'm doing what I'm "supposed to" do. I welcome any thoughts.

My son is five weeks old. We start his feedings on the breast, and he'll go anywhere from 5 to 20 minutes. He always needs formula after (we're supposed to supplement with Neosure anyway). I seem to have a very paltry supply. Based on what I get when I pump, and what he eats when he just takes a bottle, I seem to produce, at most, a bit over an ounce per feeding. So many women seem to get ounces and ounces per session!

And I wonder what the real benefit is of doing all this. He's obviously getting some breast milk, but most of what he eats is formula. He's growing well and seems content. Getting him to take the breast (with nipple shield) frequently involves a protracted wrestling match. Pumping is a nightmare, so I'd prefer to feed him from the tap as much as possible, but given my low supply, anyway, am I doing this for him or for me? I've tried Mother's milk tea, and such, to no avail.

I'd like to continue until I go back to work at 4 months, but not if it really isn't benefitting him much, given that I sort of hate it. But I'm having a hard time finding guidance that isn't pushing one agenda or another.