Well nobody knows why they wanted to capture her. However from the few possibilities it would either be:
1. cause she was a spy with important information and hidden jutsu from their country, they didn't want enemy to have it.
2. from a rare clan with many secrets that they were after, though this wouldn't make sense when cause nothing is more rare than sharingan, so they would rather go for that.
3. she could be under some kind of technique. We have seen the mind transfer techniques, so it could be someone important stealing her body though this is a far fetched guess of mine xD
4. the most likely is that she has some information they want. for that they would need her alive, but how they would know she has it and what it is, is impossible to say.
The highest possibility however is that it might be a setup by Madara, who just told some mist nins a big lie to make them hunt down rin, and then he sent some weak ones so obito could handle it. And how he set it up I can't answer cause it would need a longer and new thread, but to make it short, he has some sort of control over kiri probably through black zetsu
