tl;dr: Essentially, Cosima is partly pissed because they're using a child as a stem cell donor, but mostly pissed because she's being used as a pawn to force Sarah to cooperate with Leda
It's hard to answer this question without revealing the spoiler, since it's the entire reason Cosima was so angry:
She's mad because the stem cells came from a child, and because Leda is using her (Cosima) to try and keep that child close by.
Stem cells come from bone marrow, which is only found deep inside of bones. In reality, Kira's tooth wouldn't have even worked: tooth root is not bone marrow, and has no stem cells. But even if we give them a pass here, Kira has a finite number of teeth. The traditional way to get bone marrow from a person is extremely painful: a large needle is forced through the femur bone and marrow extracted, like drawing blood. In addition, taking too much bone marrow from a person can have adverse side effects: marrow is the source of our immune system, for example.
Growing stem cells is possible, but expensive and difficult, but Cosima probably assumed that Leda had figured out how to do it, and that she was the beneficiary of that technology. Even if they did have to harvest, if the marrow donor were an adult, that person could legally and morally consent, with full knowledge of the problems and complications. That person would, in theory, make a voluntary and willing choice to donate marrow.
Instead, she finds out that they took the marrow from a child; and once Kira runs out of teeth, if they need any more, they'll have to take it from her the hard way. Although Kira is shown to be fairly precocious, she's still too young to really understand what she's offering to do. Instead, in Cosima's mind, Leda is playing on Kira's desire to help her aunt and do something good, not really knowing the consequences.
Even worse, though, is that now Kira knows that she's the only one who can help Cosima get better. Not only is Leda using Kira to cure Cosima, they're using Cosima's illness to get their hooks into both Kira and Sarah. As long as Kira thinks Cosima might need more of her teeth, or marrow, or whatever, she's going to want to help. And Sarah's going to want to let her, if only to keep Cosima from dying.