Some civil cases are tried by jury, but I never talked about civil juries, just the level of proof. We hear a lot about civil cases so it's not unreasonable for people to imagine trials where two people tell a story and the "winner" is the one who is believed.
As for the conclusion - the burden of proof is one way. Quite rightly, people aren't sent to prison based on a close decision. You can end a case, thinking that someone is probably guilty, but if there's doubt you don't convict them.
This isn't controversial stuff - it's quite literally what happens in a criminal case. It's tough on the defendant that the decision isn't the same as "innocent", but if the court had to prove innocence instead of guilt, they would be more likely to end up in prison, so it's ultimately to their benefit. If it meant that everyone else was lying (which was the conclusion that some have come to), then nearly every case would end with the other witnesses/victims being prosecuted. Clearly that's only happens very rarely.