'Although' in the Bible

We are not commending ourselves to you again, but are giving you an occasion to be [rightfully] proud of us, so that you will have an answer for those who take pride in [outward] appearances [the virtues they pretend to have] rather than what is [actually] in heart.

So even though I wrote to you [as I did], it was not for the sake of the offender nor for the sake of the one offended, but in order to make evident to you before God how earnestly you do care for us [and your willingness to accept our authority].