Paul is so committed to seeing people trust Jesus he puts forth maximum effort to help people do that. He wants nothing in his life to become an obstacle. He also tells us we should not become yoked, or linked in a way that cannot easily be broken to a non-Christian. A Christian’s life should be too different from a non-Christian’s for that to work.
The reason we shouldn’t be yoked to a non-Christian is because it is impossible for people traveling in different directions to travel together. On the other hand, we are yoked to Jesus. By being yoked to him, we should find it easier to go in the right direction. We also need to recognize that our reputation reflects on Jesus and make sure we are not creating barriers to him in the way we act.